{"id":25610,"date":"2022-04-04T10:18:04","date_gmt":"2022-04-04T04:48:04","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=25610"},"modified":"2022-04-07T11:34:42","modified_gmt":"2022-04-07T06:04:42","slug":"big-ideas-math-answers-grade-6-chapter-7","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6-chapter-7\/","title":{"rendered":"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume"},"content":{"rendered":"<p>Wanna get the best preparatory material of Big Ideas Math 6th Grade Chapters? If yes, then you have hit the exact page. Here, in this article, we are providing in-depth concepts of area, surface area, and volume. You can understand all the concepts with the help of Big Ideas Math Book Solutions. We are providing the step-by-step procedure and its explanations for all the problems using the tips and figures. Follow Big Ideas Math Book\u00a0 6th Grade Answer Key Chapter 7 and know shortcuts, time management, etc. Understand all the concepts of area, surface area, and volume in Big Ideas Math Book Solution Key. Click on the below-given pdf links of <b><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6\/\">Big Ideas Math Answers Grade 6<\/a> Chapter 7<\/b> and get the solutions here.<\/p>\n<h2>Big Ideas Math Book 6th Grade Answer Key Chapter 7 Area, Surface Area, and Volume<\/h2>\n<p>To excel in the exam, candidates of 6th standard have to refer to the important preparatory material of Big Ideas Math Book Answer Key Grade 6 Chapter 7 Area, Surface Area, and Volume. If you facing difficulty in solving or calculating the problems, you can easily understand them with the help of <b>Big Ideas Math Book Answer Key Chapter 7<\/b>. Check the below sections to know the performance, various chapters involved in this concept. You can find the various chapters like area of parallelograms, area of triangles, areas of trapezoids, three-dimensional figures, and so on.<\/p>\n<p><strong>Performance<\/strong><\/p>\n<ul>\n<li><a href=\"#Area,_Surface_Area,_and_Volume_STEAM_Video\/Performance\">Area, Surface Area, and Volume STEAM Video\/Performance<\/a><\/li>\n<li><a href=\"#Area,_Surface_Area,_and_Volume_Gettig_Ready_for_chapter_7\">Area, Surface Area, and Volume Gettig Ready for chapter 7<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Areas of Parallelograms<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.1_Areas_of_Parallelograms\">Lesson 7.1 Areas of Parallelograms<\/a><\/li>\n<li><a href=\"#Areas_of_Parallelograms_Homework_&amp;_Practice_7.1\">Areas of Parallelograms Homework &amp; Practice 7.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Areas of Triangles<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.2_Areas_of_Triangles\">Lesson 7.2 Areas of Triangles<\/a><\/li>\n<li><a href=\"#Areas_of_Triangles_Homework_&amp;_Practice_7.2\">Areas of Triangles Homework &amp; Practice 7.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Areas of Trapezoids and Kites<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.3_Areas_of_Trapezoids_and_Kites\">Lesson 7.3 Areas of Trapezoids and Kites<\/a><\/li>\n<li><a href=\"#Areas_of_Trapezoids_and_Kites_Homework_&amp;_Practice_7.3\">Areas of Trapezoids and Kites Homework &amp; Practice 7.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Three-Dimensional Figures<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.4_Three_Dimensional_Figures\">Lesson 7.4 Three-Dimensional Figures<\/a><\/li>\n<li><a href=\"#Three_Dimensional_Figures_Homework_&amp;_Practice_7.4\">Three-Dimensional Figures Homework &amp; Practice 7.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Surface Areas of Prisms<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.5_Surface_Areas_of_Prisms\">Lesson 7.5 Surface Areas of Prisms<\/a><\/li>\n<li><a href=\"#Surface_Areas_of_Prisms_Homework_&amp;_Practice_7.5\">Surface Areas of Prisms Homework &amp; Practice 7.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Surface Areas of Pyramids<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.6_Surface_Areas_of_Pyramids\">Lesson 7.6 Surface Areas of Pyramids<\/a><\/li>\n<li><a href=\"#Surface_Areas_of_Pyramids_Homework_&amp;_Practice_7.6\">Surface Areas of Pyramids Homework &amp; Practice 7.6<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 7 Volumes of Rectangular Prisms<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.7_Volumes_of_Rectangular_Prisms\">Lesson 7.7 Volumes of Rectangular Prisms<\/a><\/li>\n<li><a href=\"#Volumes_of_Rectangular_Prisms_Homework_&amp;_Practice_7.7\">Volumes of Rectangular Prisms Homework &amp; Practice 7.7<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 7 &#8211; Area, Surface Area, and Volume<\/strong><\/p>\n<ul>\n<li><a href=\"#Area,_Surface_Area,_and_Volume_Connecting_Concepts\">Area, Surface Area, and Volume Connecting Concepts<\/a><\/li>\n<li><a href=\"#Area,_Surface_Area,_and_Volume_Practice_Test\">Area, Surface Area, and Volume Practice Test<\/a><\/li>\n<li><a href=\"#Area,_Surface_Area,_and_Volume_Cumulative_Practice\">Area, Surface Area, and Volume Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Area,_Surface_Area,_and_Volume_STEAM_Video\/Performance\"><\/a>Area, Surface Area, and Volume STEAM Video\/Performance<\/h3>\n<p><strong>Packaging Design<\/strong><\/p>\n<p>Surface area can be used to determine amounts of materials needed to create objects. Describe another situation in which you need to \ufb01nd the surface area of an object.<\/p>\n<p>Watch the STEAM Video \u201cPackaging Design.\u201d Then answer the following questions. Alex is cutting a design out of paper and folding it to form a box.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25963\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 1\" width=\"291\" height=\"306\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-1.png 291w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-1-285x300.png 285w\" sizes=\"(max-width: 291px) 100vw, 291px\" \/><\/p>\n<p>Question 1.<br \/>\nTory says that the length of the design is 47 inches and the width is 16 inches. Show several ways that you can arrange three of the designs on a roll of paper that is 48 inches wide. You can make the length of the paper as long as is needed.<\/p>\n<p>Answer:<br \/>\nWe can make the length of the paper = 15.6666 inches<\/p>\n<p>Explanation:<br \/>\nGiven that the length of the design = 47 inches<br \/>\nthat the width of the design = 16 inches<br \/>\narea of the design = 752 inches<br \/>\nThey can arrange the three of the design on a roll of paper that = 48 inches<br \/>\n(752\/48)<br \/>\n15.6666 inches<br \/>\nQuestion 2.<br \/>\nTory says that the cut-out design has an area of 619 square inches. What is the least possible amount of paper that is wasted when you cut out three of the designs?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 2\" width=\"309\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-2.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-2-300x196.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>Answer:<br \/>\nThe least amount of paper that is wasted when you cut out three of the designs = 12.89<\/p>\n<p>Explanation:<br \/>\nThe area of the rectangle = breadth x height<br \/>\n619 square inches = 48 in x length<br \/>\n619 = 48l<br \/>\nl = 619\/48<br \/>\nl = 12.89<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Maximizing the Volumes of Boxes<\/strong><\/p>\n<p>After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given the dimensions of a small box and two larger boxes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25967\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-3.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 3\" width=\"283\" height=\"146\" \/><br \/>\nYou will be asked to determine how many small boxes can be placed in each larger box. When a company is deciding on packaging for a product, why should the surface area of the packaging also be considered?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25968\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-4.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 4\" width=\"287\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-4.png 287w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-4-232x300.png 232w\" sizes=\"(max-width: 287px) 100vw, 287px\" \/><\/p>\n<h3><a id=\"Area,_Surface_Area,_and_Volume_Gettig_Ready_for_chapter_7\"><\/a>Area, Surface Area, and Volume Gettig Ready for chapter 7<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p>The formulas for the areas of polygons can be derived from one area formula, the area of a rectangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-5.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 5\" width=\"576\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-5.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-5-300x92.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Work with a partner. Find (a) the dimensions of the \ufb01gures and (b) the areas of the \ufb01gures. What do you notice?<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-6.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 6\" width=\"407\" height=\"101\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-6.png 407w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-6-300x74.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the rectangle = The product of the length and the product of the width<br \/>\nThe area of the parallelogram = the product of the width and the product of the height<\/p>\n<p>Explanation:<br \/>\nThe area of the rectangle is equal to the area of the parallelogram<br \/>\nThe area of the rectangle = the product of the length and the product of the width<br \/>\nThe area of the rectangle = length x width<br \/>\narea = l x w<br \/>\nThe area of the parallelogram = the product of the base and the product of the width<br \/>\narea = base x height<br \/>\narea = b x h<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25971\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-7.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 7\" width=\"356\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-7.png 356w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-7-300x93.png 300w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<p>Answer:<br \/>\nThe\u00a0 area of the rectangle = the product of the length and the product of the width<br \/>\nThe area of the parallelogram = (1\/2) x the product of the base and the product of the height<\/p>\n<p>Explanation:<br \/>\nThe area of the rectangle is equal to the area of the parallelogram<br \/>\nThe area of the rectangle = the product of the length and the product of the width<br \/>\nThe area of the rectangle = length x width<br \/>\narea = l x w<br \/>\nThe area of the triangle =(1\/2) x\u00a0 the product of the base and the product of the width<br \/>\narea =(1\/2) base x height<br \/>\narea =(1\/2) b x h<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-8.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 8\" width=\"350\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-8.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-8-300x92.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/p>\n<p>Answer:<br \/>\nThe\u00a0 area of the rectangle = the product of the length and the product of the width<br \/>\nThe area of the trapezoid = (1\/2) x height x (base 1 + base 2)<\/p>\n<p>Explanation:<br \/>\nThe area of the rectangle is equal to the area of the parallelogram<br \/>\nThe area of the rectangle = the product of the length and the product of the width<br \/>\nThe area of the rectangle = length x width<br \/>\narea = l x w<br \/>\nThe area of the trapezoid =(1\/2) x product of the height\u00a0 and the product of the bases<br \/>\narea =(1\/2) x height x bases<br \/>\narea =(1\/2) x height (b1 + b2)<\/p>\n<p><strong>Vocabulary<\/strong><\/p>\n<p>The following vocabulary terms are de\ufb01ned in this chapter. Think about what each term might mean and record your thoughts.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-9.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 9\" width=\"370\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-9.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-9-300x49.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<h3><a id=\"Lesson_7.1_Areas_of_Parallelograms\"><\/a>Lesson 7.1 Areas of Parallelograms<\/h3>\n<p>A polygon is a closed \ufb01gure in a plane that is made up of three or more line segments that intersect only at their endpoints. Several examples of polygons are parallelograms, rhombuses, triangles, trapezoids, and kites.<br \/>\nThe formula for the area of a parallelogram can be derived from the de\ufb01nition of the area of a rectangle. Recall that the area of a rectangle is the product of its length \u2113 and its width w. The process you use to derive this and other area formulas in this chapter is called deductive reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-10.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 10\" width=\"142\" height=\"212\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Deriving the Area Formula of a Parallelogram<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Draw any rectangle on a piece of centimeter grid paper. Cut the rectangle into two pieces that can be arranged to form a parallelogram. What do you notice about the areas of the rectangle and the parallelogram?<br \/>\nb. Copy the parallelogram below on a piece of centimeter grid paper. Cut the parallelogram and rearrange the pieces to \ufb01nd its area.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-11.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 11\" width=\"430\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-11.png 430w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-11-300x157.png 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-12.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 12\" width=\"162\" height=\"199\" \/><br \/>\nc. Draw any parallelogram on a piece of centimeter grid paper and \ufb01nd its area. Does the area change when you use a different side as the base? Explain your reasoning.<br \/>\nd. Use your results to write a formula for the area A of a parallelogram.<\/p>\n<p>Answer:<br \/>\nc : The area of the parallelogram = the product of the width and the product of the height<br \/>\narea = width x height<br \/>\narea = w x h<br \/>\nYes the area changes.<br \/>\nWe use the bases as equal length and width as equal length<br \/>\nd : the area of the parallelogram = the product of the width and the product of the height<\/p>\n<p>c : The area of the parallelogram = the product of the width and the product of the height<br \/>\narea = width x height<br \/>\narea = w x h<br \/>\nYes the area changes.<br \/>\nWe use the bases as equal length and width as equal length<br \/>\nd : the area of the parallelogram = the product of the width and the product of the height<\/p>\n<p><strong>7.1 Lesson<\/strong><\/p>\n<p>The area of a polygon is the amount of surface it covers. You can \ufb01nd the area of a parallelogram in much the same way as you can \ufb01nd the area of a rectangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-13.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 13\" width=\"208\" height=\"78\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-13.1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 13.1\" width=\"734\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-13.1.png 734w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-13.1-300x83.png 300w\" sizes=\"(max-width: 734px) 100vw, 734px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Find the area of the parallelogram.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-14.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 14\" width=\"125\" height=\"133\" \/><\/p>\n<p>Answer:<br \/>\nArea = 500 m<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base b and its height h.<br \/>\narea = b x h<br \/>\nb = 20 m, h = 25 m<br \/>\nSo the Area of the parallelogram = 500 m<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-15.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 15\" width=\"118\" height=\"143\" \/><\/p>\n<p>Answer;<br \/>\nArea = 126 in<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of base b and its height h<br \/>\narea = b x h<br \/>\nb = 7 in , h = 18 in<br \/>\nSo area = 126 in<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-16.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 16\" width=\"124\" height=\"142\" \/><\/p>\n<p>Answer:<br \/>\n615 yd<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of base b and its height h<br \/>\narea = b x h<br \/>\nb = 30 yd, h = 20.5 yd<br \/>\nSo area = 615 yd<\/p>\n<p>When \ufb01nding areas, you may need to convert square units. The diagrams at the left show that there are 9 square feet per square yard.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-17.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 17\" width=\"218\" height=\"108\" \/><br \/>\n1 yd<sup>2<\/sup> = (1 yd)(1 yd) = (3 ft)(3 ft) = 9 ft<sup>2<\/sup><br \/>\nYou can use a similar procedure to convert other square units.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 4.<br \/>\nFind the area of the parallelogram in square centimeters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-18.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 18\" width=\"150\" height=\"145\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\nArea = 400 cms<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\narea = base x height<br \/>\narea = 4 m x 10 m<br \/>\narea = 40 m<br \/>\n1 meter = 100 centimeters<br \/>\n40 meter = 400 centimeters<br \/>\narea = 400 cm<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to use the area of a rectangle to \ufb01nd the area of a parallelogram<\/p>\n<p>Answer:<br \/>\nArea of the rectangle = length x breadth<br \/>\nArea of the parallelogram =\u00a0 \u00a0base x height<\/p>\n<p>Explanation:<br \/>\nArea of the rectangle = length x breadth<br \/>\narea = l x b<br \/>\nArea of the parallelogram =\u00a0 \u00a0base x height<br \/>\narea =\u00a0 b x h<br \/>\narea =\u00a0 bh<\/p>\n<p><strong>FINDING AREA<\/strong><br \/>\nFind the area of the parallelogram.<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-19.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 19\" width=\"251\" height=\"86\" \/><\/p>\n<p>Answer:<br \/>\narea = 80 ft<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\narea = base x height<br \/>\narea = b x h<br \/>\nb = 16 ft and h = 5 ft given<br \/>\narea = 16 x 5<br \/>\narea = 80 ft<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-20.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 20\" width=\"130\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = 14 . 4 km<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\narea = base x height<br \/>\narea = b x h<br \/>\nb = 3 km and h = 4.8 km given<br \/>\narea = 3 x 4.8<br \/>\narea = 14.4 km<\/p>\n<p>Question 8.<br \/>\n<strong>REASONING<\/strong><br \/>\nDraw a parallelogram that has an area of 24 square inches.<\/p>\n<p>Answer:<br \/>\nWe have to assume that the base = 4 square inches and the height = 6 square inches<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\nThe side of an office building in Hamburg, Germany, is in the shape of a parallelogram. The area of the side of the building is about 2150 square meters. What is the length x of the portion of the building that extends over the river?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-21.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 21\" width=\"229\" height=\"139\" \/><\/p>\n<p>Answer:<br \/>\nThe length of the portion of the building that extends over the river = 45 m<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the bases and the product of the bases<br \/>\narea = 2150 square meters given<br \/>\narea = 25 m x (39 +47) given that height = 25 and base = 39<br \/>\narea = 25 x (86)<br \/>\narea = 2150<br \/>\nThus the length of the portion of the building that extends over the river = 45 m<\/p>\n<p>Question 10.<br \/>\nYou make a photo prop for a school fair. You cut a 10-inch square out of a parallelogram-shaped piece of wood. What is the area of the photo prop?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-22.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 22\" width=\"201\" height=\"294\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the photo prop = 32<\/p>\n<p>Explanation:<br \/>\nthe area of the photo prop = the product of the base and the product of the height<br \/>\narea = h x b<br \/>\narea = 8 x 4<br \/>\narea = 32 ft<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA galaxy contains a parallelogram-shaped dust \ufb01eld. The dust \ufb01eld has a base of 150 miles. The height is 14% of the base. What is the area of the dust \ufb01eld?<\/p>\n<p>Answer:<br \/>\nThe area of the dust field =3,150<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the height and the product of the base<br \/>\narea = h x b given that height = 14% = (14\/100) x 150 = 21, base = 150 miles<br \/>\narea = 3150<\/p>\n<h3><a id=\"Areas_of_Parallelograms_Homework_&amp;_Practice_7.1\"><\/a>Areas of Parallelograms Homework &amp; Practice 7.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Graph the equation.<\/p>\n<p>Question 1.<br \/>\ny = 4x<\/p>\n<p>Answer:<br \/>\n:<img loading=\"lazy\" class=\"alignnone size-medium wp-image-30531\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-27-273x300.png\" alt=\"\" width=\"273\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-27-273x300.png 273w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-27.png 392w\" sizes=\"(max-width: 273px) 100vw, 273px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given equation = y = 4x<br \/>\nfor suppose x = 0, then y = 0<br \/>\nx = 1 , then y = 4 that means (1,4) y = 4 x 1 = 4<br \/>\nx = 2 , then y = 8 that means (2,8) y = 4 x 2 = 8<br \/>\nx = 3 , then y = 12 that means (3,12) y = 4 x 3 = 12<\/p>\n<p>Question 2.<br \/>\ny = x + 3<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-30532\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-28-222x300.png\" alt=\"\" width=\"222\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-28-222x300.png 222w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-28.png 325w\" sizes=\"(max-width: 222px) 100vw, 222px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given equation = y = x + 3<br \/>\nfor suppose x = 0, then y = 3<br \/>\nx = 1 , then y = 4 that means (1,4) y = 1 + 3 = 4<br \/>\nx = 2 , then y = 5 that means (2, 5) y = 2 + 3\u00a0 = 5<br \/>\nx = 3 , then y = 6 that means (3,16) y = 3 + 3 = 6<br \/>\nx = 4 , then y = 7 that means (4, 7) y = 4 + 3 = 7<\/p>\n<p>Question 3.<br \/>\ny = 2x + 5<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-30535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-29-226x300.png\" alt=\"\" width=\"226\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-29-226x300.png 226w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-29.png 319w\" sizes=\"(max-width: 226px) 100vw, 226px\" \/><\/p>\n<p>Explanation:<br \/>\nThe given equation = y = 2x + 5<br \/>\nfor suppose x = 0, then y = 5<br \/>\nx = 1 , then y = 7 that means (1,7) y = 2 + 5 = 7<br \/>\nx = 2 , then y = 9 that means (2, 9) y = 4 + 5\u00a0 = 9<br \/>\nx = 3 , then y = 11 that means (3,11) y = 6 + 5 = 11<br \/>\nx = 4 , then y = 13 that means (4, 13) y = 8 + 5 = 13<\/p>\n<p><strong>Represent the ratio relationship using a graph.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-23.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 23\" width=\"242\" height=\"74\" \/><\/p>\n<p>Answer:<br \/>\n1: 2 ratio<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-30524\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-25-300x267.png\" alt=\"\" width=\"300\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-25-300x267.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-25.png 467w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-24.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 24\" width=\"292\" height=\"78\" \/><\/p>\n<p>Answer:<br \/>\n1 : 2 ratio<\/p>\n<p>Explanation:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-30525\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-26-257x300.png\" alt=\"\" width=\"257\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-26-257x300.png 257w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-26.png 411w\" sizes=\"(max-width: 257px) 100vw, 257px\" \/><\/p>\n<p><strong>Write the prime factorization of the number.<\/strong><\/p>\n<p>Question 6.<br \/>\n55<\/p>\n<p>Answer:<br \/>\n5 . 11<\/p>\n<p>Explanation:<br \/>\n5 x 11 = 55<br \/>\nS0 5,11<\/p>\n<p>Question 7.<br \/>\n60<\/p>\n<p>Answer:<br \/>\n2 x 2 x 3 x 5<\/p>\n<p>Explanation:<br \/>\n2 x 30 = 60<br \/>\n2 x 15 = 30<br \/>\n5 x 3 = 15<br \/>\n3 x 1 = 3<\/p>\n<p>Question 8.<br \/>\n150<\/p>\n<p>Answer:<br \/>\n3 . 5 . 5 . 2<\/p>\n<p>Explanation:<br \/>\n3 x 50 = 150<br \/>\n5 x 10 = 50<br \/>\n5 x 2 = 10<br \/>\n2 x 1 = 2<\/p>\n<p>Question 9.<br \/>\n126<\/p>\n<p>Answer:<br \/>\n2 . 3 . 3 . 7<\/p>\n<p>Explanation:<br \/>\n2 x 63 = 126<br \/>\n3 x 21 = 63<br \/>\n3 x 7 = 21<br \/>\n7 x 1 = 7<\/p>\n<p><strong>Add or subtract.<\/strong><\/p>\n<p>Question 10.<br \/>\n2.36 + 15.71<\/p>\n<p>Answer:<br \/>\n2.36 + 15.71 = 18.07<\/p>\n<p>Explanation:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-22.png\" alt=\"\" width=\"180\" height=\"131\" \/><br \/>\nQuestion 11.<br \/>\n9.035 &#8211; 6.144<\/p>\n<p>Answer:<br \/>\n9.035 &#8211; 6.144 = 2.891<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-23.png\" alt=\"\" width=\"258\" height=\"200\" \/><\/p>\n<p>Question 12.<br \/>\n28.351 &#8211; 19.3518<\/p>\n<p>Answer:<br \/>\n28.351 = 19.3518 = 8.9992<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-30315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-24-300x177.png\" alt=\"\" width=\"300\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-24-300x177.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7-percents-4.2-24.png 334w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>USING TOOLS<\/strong><br \/>\n<strong>Rearrange the parallelogram as a rectangle. Then \ufb01nd the area.<\/strong> (See Exploration 1, p. 285.)<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-25.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 25\" width=\"185\" height=\"85\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-69-1.png\" alt=\"\" width=\"253\" height=\"140\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-26.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 26\" width=\"120\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32645\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-71.png\" alt=\"\" width=\"167\" height=\"148\" \/><\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-27.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 27\" width=\"201\" height=\"153\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-72-300x122.png\" alt=\"\" width=\"300\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-72-300x122.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-72.png 339w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>FINDING AREA<\/strong><br \/>\n<strong>Find the area of the parallelogram.<\/strong><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-28.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 28\" width=\"196\" height=\"102\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = 18 ft<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the height<br \/>\narea = b x h given that base = 6 ft height = 3 ft<br \/>\narea = 18 ft<br \/>\nQuestion 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-29.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 29\" width=\"143\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = 840 mm<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the height<br \/>\narea = b x h given that base = 20 mm height = 42 ft<br \/>\narea = 840 mm<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-30.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 30\" width=\"171\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = 187 km<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the height<br \/>\narea = b x h given that base = 17 km height = 11km<br \/>\narea = 187 km<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-31.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 31\" width=\"161\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = 3750 cm<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the height<br \/>\narea = b x h given that base = 75 cm\u00a0 height = 50 cm<br \/>\narea = 3750 cm<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-32.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 32\" width=\"164\" height=\"127\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = 243 in<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the height<br \/>\narea = b x h given that base = 13.5 in\u00a0 height = 18 in<br \/>\narea = 243 in<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-33.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 33\" width=\"142\" height=\"190\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = 894 mi<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the height<br \/>\narea = b x h given that base = 24 in, height = 37 x (1\/4)<br \/>\narea = 24 x 37.25<br \/>\narea = 894 mi<\/p>\n<p>Question 22.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the area of the parallelogram. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-34.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 34\" width=\"321\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-34.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-34-300x146.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\n<p>Answer:<br \/>\nYes my friend is correct<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\narea = 8 m x 15 m<br \/>\nGiven that base = 8m and height = 15 m<br \/>\narea = base x height<br \/>\narea = 8 m x 15 m<br \/>\narea = 120 m<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA ceramic tile in the shape of a parallelogram has a base of 4 inches and a height of 1.5 inches. What is the area of the tile?<\/p>\n<p>Answer:<br \/>\nThe area of the tile =\u00a0 6 inches<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\narea = base x height<br \/>\narea = 4 x 1.5<br \/>\narea = 6 inches<\/p>\n<p><strong>FINDING AREA<\/strong><br \/>\n<strong>Find the area of the parallelogram. Round to the nearest hundredth if necessary.<\/strong><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-35.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 35\" width=\"176\" height=\"157\" \/><\/p>\n<p>Answer:<br \/>\n4800 cm<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\narea = base x height<br \/>\narea = 6 x 8<br \/>\narea = 48 m<br \/>\n1 meter = 100 centimeter<br \/>\n48 m = 4800 cm<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-36.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 36\" width=\"148\" height=\"164\" \/><\/p>\n<p>Answer:<br \/>\n1,121.64096<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\narea = base x height<br \/>\narea = 1320 yd x 1496 yd<br \/>\narea = 1974720yd<br \/>\n1 yard = 0.000568 mile<br \/>\n1974720 yd = 1,121.64096 miles<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-37.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 37\" width=\"164\" height=\"150\" \/><\/p>\n<p>Answer:<br \/>\n67.4 ft<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\narea = base x height<br \/>\narea = 5 m x 4 m<br \/>\narea = 20 m<br \/>\n1 meter = 3 feet 3.37 inches<br \/>\n20 m = 67 . 4 ft<\/p>\n<p>Question 27.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nYour deck has an area of 128 square feet. After adding a section, the area will be (s<sup>2<\/sup> + 128) square feet. Draw a diagram of how this can happen.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-73.png\" alt=\"\" width=\"185\" height=\"148\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou use the parallelogram-shaped sponge to create the T-shirt design. The area of the design is 66 square inches. How many times do you use the sponge to create the design? Draw a diagram to support your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-37.1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 37.1\" width=\"357\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-37.1.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-37.1-300x178.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p>Answer:<br \/>\n33 times is used to the sponge to create the design = 33<br \/>\nExplanation:<br \/>\nThe area of the parallelogram = base x height<br \/>\narea = 3 x 1<br \/>\narea = 3\u00a0 inches<br \/>\nThe area of the design = 66 inches<br \/>\n66\/3 = 33<\/p>\n<p><strong>FINDING A MISSING DIMENSION<\/strong><br \/>\n<strong>Find the missing dimension of the parallelogram described.<\/strong><\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-38.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 38\" width=\"216\" height=\"43\" \/><\/p>\n<p>Answer:<br \/>\nheight = 9 ft<br \/>\nExplanation:<br \/>\narea of the parallelogram = the product of the base and the product of the height<br \/>\narea = base x height<br \/>\narea = 6 ft\u00a0 x 9 ft<br \/>\narea = 54 ft<br \/>\nSo height = 54<\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-39.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 39\" width=\"261\" height=\"45\" \/><\/p>\n<p>Answer:<br \/>\nbase = 6.5 cm<\/p>\n<p>Explanation:<br \/>\narea of the parallelogram = the product of the base and the product of the height<br \/>\narea = base x height<br \/>\narea = 6 . 5 cm\u00a0 x 2.5 cm<br \/>\narea = 16 .25<br \/>\nSo height = 2.5 cm<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-40.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 40\" width=\"321\" height=\"43\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-40.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-40-300x40.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\n<p>Answer:<br \/>\nheight = 4 yd<\/p>\n<p>Explanation:<br \/>\n5(x + 4) = 5x + 20<\/p>\n<p>Question 32.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe staircase has three identical parallelogram-shaped panels. The horizontal distance between each panel is 4.25 inches. The area of each panel is 287 square inches. What is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-41.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 41\" width=\"215\" height=\"253\" \/><\/p>\n<p>Answer:<br \/>\nThe value of x = 14<\/p>\n<p>Explanation:<br \/>\n(1\/2)bx = 287<br \/>\n(1\/2) x 14 x x = 287<br \/>\n7x = 287<br \/>\nx = 287\/7<br \/>\nx = 41<br \/>\n50.5 -8<br \/>\n42.5 x 2 = 8.50<\/p>\n<p>Question 33.<br \/>\n<strong>LOGIC<\/strong><br \/>\nEach dimension of a parallelogram is multiplied by a positive number n. Write an expression for the area of the new parallelogram.<\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = (1\/2) x b x h<br \/>\narea = (1\/2)bn x hn<br \/>\n(1\/2) bhn<\/p>\n<p>Question 34.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nRearrange the rhombus shown to write a formula for the area of a rhombus in terms of its diagonals.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-42.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 42\" width=\"149\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the rhombus = (1\/2) ab<br \/>\narea = (1\/2) x ab<\/p>\n<p>Explanation:<br \/>\nThe area of the rhombus = (1\/2) ab<br \/>\narea = (1\/2) x ab<\/p>\n<h3><a id=\"Lesson_7.2_Areas_of_Triangles\"><\/a>Lesson 7.2 Areas of Triangles<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Deriving the Area Formula of a Triangle<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Draw any parallelogram on a piece of centimeter grid paper. Cut the parallelogram into two identical triangles. How can you use the area of the parallelogram to \ufb01nd the area of each triangle?<br \/>\nb. Copy the triangle below on a piece of centimeter grid paper. Find the area of the triangle. Explain how you found the area.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-43.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 43\" width=\"509\" height=\"271\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-43.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-43-300x160.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><br \/>\nc. Draw any acute triangle on a piece of centimeter grid paper and \ufb01nd its area. Repeat this process for a right triangle and an obtuse triangle.<br \/>\nd. Do the areas change in part(c) when you use different sides as the base? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na : The area of the parallelogram = (1\/2) x b x h<br \/>\nThe area of the triangle = base x height<br \/>\nb : The area of the triangle = base x height<br \/>\narea = b x h<br \/>\nc : The area of the acute-angled triangle = (1\/2) x b x h<br \/>\nThe area of the right-angled triangle = (1\/2) x base x perpendicular<br \/>\nThe area of the obtuse-angled triangle =(1\/2) x b x h<\/p>\n<p>Explanation:<br \/>\na : <img loading=\"lazy\" class=\"alignnone size-full wp-image-32685\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-74.png\" alt=\"\" width=\"293\" height=\"93\" \/><br \/>\nb : <img loading=\"lazy\" class=\"alignnone size-full wp-image-32747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-75.png\" alt=\"\" width=\"226\" height=\"123\" \/><br \/>\nc :<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-76.png\" alt=\"\" width=\"197\" height=\"96\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-77.png\" alt=\"\" width=\"244\" height=\"128\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-78.png\" alt=\"\" width=\"280\" height=\"157\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-44.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 44\" width=\"160\" height=\"228\" \/><br \/>\ne. Use your results to write a formula for the area A of a triangle. Use the formula to \ufb01nd the area of the triangle shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-45.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 45\" width=\"153\" height=\"146\" \/><\/p>\n<p>Answer:<br \/>\n15 m<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = half x the product of the base b and the product of the height h<br \/>\narea = (1\/2) x b x h given that b= 6 m ,h = 5 m<br \/>\narea = (1\/2) x 30<br \/>\narea = 15 m<\/p>\n<p><strong>7.2 Lesson<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-26021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-46.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 46\" width=\"735\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-46.png 735w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-46-300x86.png 300w\" sizes=\"(max-width: 735px) 100vw, 735px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the area of the triangle<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-47.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 47\" width=\"203\" height=\"95\" \/><\/p>\n<p>Answer:<br \/>\n22 ft<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) x bh<br \/>\nThe area of the triangle = (1\/2) x the product of base and the product of the height<br \/>\nb = 11 ft , h = 4 ft<br \/>\narea = (1\/2) x bh<br \/>\narea = (1\/2) x 11 x 4<br \/>\narea = (1\/2) x 44<br \/>\narea = 22 ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-48.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 48\" width=\"225\" height=\"122\" \/><\/p>\n<p>Answer:<br \/>\nArea = 60 cm<\/p>\n<p>Explanation:<br \/>\nThe area\u00a0 of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\nb = 15 cm, h = 8cm<br \/>\narea = (1\/2) x 15 x 8<br \/>\narea = (1\/2) x 120<br \/>\narea = 60<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-49.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 49\" width=\"178\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\narea = 110 m<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\nSo the b = 22m ,h= 10 m<br \/>\narea= (1\/2) x 10 x 22<br \/>\narea = (1\/2) x 220<br \/>\narea = 110 m<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-50.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 50\" width=\"181\" height=\"104\" \/><\/p>\n<p>Answer:<br \/>\n6.5 yd<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) x the product of base b and the product of the height h<br \/>\nSo the b = (13\/2) yd h = 2 yd<br \/>\narea = (1\/2) x b x h<br \/>\narea = (1\/2) x 6.5 x 2<br \/>\narea = (1\/2) x 13<br \/>\narea = 6.5<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the missing dimension of the triangle.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-51.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 51\" width=\"200\" height=\"103\" \/><\/p>\n<p>Answer:<br \/>\nBase = 8 cm<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle =(1\/2) x\u00a0 the product of the base b and the product of height h<br \/>\narea of the triangle = 24 cm given<br \/>\nSo the height = 6cm given<br \/>\narea =\u00a0 (1\/2) x b x h<br \/>\narea = (1\/2) x 8 x 6<br \/>\narea = (1\/2) x 48<br \/>\narea = 24<br \/>\nSo base = 8 cm<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-52.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 52\" width=\"186\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nheight = 17.5ft<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle =(1\/2) x\u00a0 the product of the base b and the product of the height h<br \/>\narea of the triangle = 175 ft given,<br \/>\nSo we have to find the height?<br \/>\narea = (1\/2) x 20 x 17.5<br \/>\narea = (1\/2) x 350<br \/>\narea = 175<br \/>\nSo the height = 17.5 ft<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\n<strong>FINDING AREA<\/strong><br \/>\nFind the area of the triangle at the left.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-53.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 53\" width=\"160\" height=\"102\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 12<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) x the product of base and the product of the height<br \/>\nb = 8 , h = 3<br \/>\narea = (1\/2) x bh<br \/>\narea = (1\/2) x 8 x 3<br \/>\narea = (1\/2) x 24<br \/>\narea = 12<\/p>\n<p>Question 8.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to use the area of a parallelogram to \ufb01nd the area of a triangle.<\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\nThe area of the triangle = half x\u00a0 the product of the base b and the product of the height h<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\narea = b x h<br \/>\nThe area of the triangle = half x the product of the base and the height<br \/>\narea = (1\/2) x b x h<br \/>\n<strong>FINDING A MISSING DIMENSION<\/strong><br \/>\n<strong>Find the missing dimension of the triangle.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-54.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 54\" width=\"200\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nbase = 10 mm<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) the product of the base and the product of the height<br \/>\narea = (1\/2) x base x height<br \/>\narea = (1\/2) x 10 mm x 6 mm<br \/>\narea = (1\/2) x 60 mm<br \/>\narea = 30 mm<br \/>\nSo base = 10 mm<br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-55.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 55\" width=\"201\" height=\"119\" \/><\/p>\n<p>A composite \ufb01gure is made up of triangles, squares, rectangles, and other two-dimensional \ufb01gures. To \ufb01nd the area of a composite \ufb01gure, separate it into \ufb01gures with areas you know how to \ufb01nd. This is called decomposition.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 11.<br \/>\nA wildlife conservation group buys the 9 square miles of land shown. What is the distance from Point A to Point B?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-56.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 56\" width=\"238\" height=\"180\" \/><\/p>\n<p>Answer:<br \/>\nThe distance from point A to point B = 3 miles<\/p>\n<p>Explanation:<br \/>\nThe\u00a0 area of the triangle = (1\/2) ab<br \/>\nGiven that\u00a0 the land shown = 9 square miles<br \/>\n(1\/2)bh = triangle ABC + triangle BCD<br \/>\n(3\/2)b + (3\/2)b = 9<br \/>\n(6\/2)b = 9<br \/>\n3 b = 9<br \/>\nb = 3 miles<br \/>\nQuestion 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nFind the area of the side of the chimney. Explain how you found the area.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-57.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 57\" width=\"125\" height=\"266\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the chimney = 31.5 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe area of the chimney = (1\/2) x base x height<br \/>\narea = (1\/2)\u00a0 x 3 x 21<br \/>\narea = 31.5 sq. ft<\/p>\n<h3><a id=\"Areas_of_Triangles_Homework_&amp;_Practice_7.2\"><\/a>Areas of Triangles Homework &amp; Practice 7.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the area of the parallelogram.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-58.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 58\" width=\"179\" height=\"93\" \/><\/p>\n<p>Answer:<span style=\"font-size: 16px; font-style: normal; font-weight: 400;\"> \u00a0<\/span><br \/>\nThe area of the parallelogram = 72 in<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = product of the height h and the product of the base b<br \/>\nb = 12 in, h = 6 in given<br \/>\narea =\u00a0 12 x 6<br \/>\narea = 72 in<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-59.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 59\" width=\"166\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = 10.5 km<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base b and the product of the height h<br \/>\nb = 3.5 km, h = 3km given<br \/>\narea = 3.5 x 3<br \/>\narea = 10.5 km<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-60.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 60\" width=\"162\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = 255 mi<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base b and the product of the height h<br \/>\nb = 17 mi, h = 15 mi given<br \/>\narea = 17 x 15<br \/>\narea = 255 mi<\/p>\n<p><strong>Tell which property the statement illustrates.<\/strong><\/p>\n<p>Question 4.<br \/>\nn . 1 = n<\/p>\n<p>Answer:<br \/>\nThe product of x = the product of y<\/p>\n<p>Explanation:<br \/>\nThe product of x = n x 1 = n<br \/>\nthe product of y = n<br \/>\nn = n<\/p>\n<p>Question 5.<br \/>\n4 . m = m . 4<\/p>\n<p>Answer:<br \/>\nThe product of x = the product of y<\/p>\n<p>Explanation:<br \/>\nThe product of x = m x 4 = 4 m<br \/>\nthe product of y = m x 4 = 4 m<br \/>\n4 . m = m . 4<\/p>\n<p>Question 6.<br \/>\n(x + 2) + 5 = x + (2 + 5)<\/p>\n<p>Answer:<br \/>\nThe product of x = the product of y<\/p>\n<p>Explanation:<br \/>\nThe product of x = (x + 2) + 5<br \/>\nthe product of y =\u00a0 x + (2 +5)<br \/>\n(x +2) +5 = x + (2 +5)<\/p>\n<p>Question 7.<br \/>\nWhat is the \ufb01rst step when using order of operations?<br \/>\nA. Multiply and divide from left to right.<br \/>\nB. Add and subtract from left to right.<br \/>\nC. Perform operations in grouping symbols.<br \/>\nD. Evaluate numbers with exponents.<\/p>\n<p>Answer:<br \/>\nEvaluate numbers with exponents<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING TOOLS<\/strong><br \/>\n<strong>Find the area of the triangle by forming a parallelogram.<\/strong> (See Exploration 1, p. 291.)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-61.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 61\" width=\"184\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the right angled triangle = (1\/2) x ab<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-77.png\" alt=\"\" width=\"244\" height=\"128\" \/><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-62.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 62\" width=\"183\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nobtused angled triangle = (1\/2) x b xh<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-78.png\" alt=\"\" width=\"280\" height=\"157\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-63.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 63\" width=\"111\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\nacute angled triangle<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-76.png\" alt=\"\" width=\"197\" height=\"96\" \/><\/p>\n<p><strong>FINDING AREA<\/strong><br \/>\n<strong>Find the area of the triangle.<\/strong><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-64.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 64\" width=\"141\" height=\"146\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 6 cm<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\narea = (1\/2) x b x h<br \/>\nSo b = 3 cm , h = 4 cm<br \/>\narea = (1\/2) x 3 x 4<br \/>\narea = (1\/2) x 12<br \/>\narea = 6 cm<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-65.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 65\" width=\"206\" height=\"91\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 90 mi<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\narea = (1\/2) x b x h<br \/>\nSo b = 20 mi\u00a0 , h = 9 mi<br \/>\narea = (1\/2) x 20 x 9<br \/>\narea = (1\/2) x 180<br \/>\narea = 90 sq. miles<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-66.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 66\" width=\"218\" height=\"156\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle =1620 in<\/p>\n<p>Explanation:<\/p>\n<p>Area of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\narea = (1\/2) x b x h<br \/>\nSo b =60 in , h = 54 in<br \/>\narea = (1\/2) x 3240<br \/>\narea = 1620 in<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-67.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 67\" width=\"142\" height=\"137\" \/><\/p>\n<p>Answer:<\/p>\n<p>The area of the triangle = 189 mm<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\narea = (1\/2) x b x h<br \/>\nSo b =21 mm , h = 18 mm<br \/>\narea = (1\/2) x 378<br \/>\narea = 189 mm<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-68.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 68\" width=\"118\" height=\"165\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 1125 cm<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\narea = (1\/2) x b x h<br \/>\nSo b =75 cm , h = 30 cm<br \/>\narea = (1\/2) x 2250<br \/>\narea = 1125 cm<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-69.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 69\" width=\"173\" height=\"71\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 132 m<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\narea = (1\/2) x b x h<br \/>\nSo b =8 m , h = 33 m<br \/>\narea = (1\/2) x 264<br \/>\narea = 132 m<\/p>\n<p>Question 17.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the area of the triangle. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-70.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 70\" width=\"324\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-70.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-70-300x144.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><\/p>\n<p>Answer:<br \/>\nYes my friend is correct<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\narea = (1\/2) x b x h<br \/>\nSob =10 m , h = 12 m<br \/>\narea = (1\/2) x 120<br \/>\narea = 60 m<\/p>\n<p>Question 18.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nEstimate the area of the cottonwood leaf.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-71.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 71\" width=\"238\" height=\"167\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the cottonwood leaf = 10 in<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\narea = (1\/2) x b x h<br \/>\nSob = 5 in , h =\u00a0 4 in<br \/>\narea = (1\/2) x 20<br \/>\narea = 10 in<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA shelf has the shape of a triangle. The base of the shelf is 36 centimeters, and the height is 18 centimeters. Find the area of the shelf in square inches.<\/p>\n<p>Answer:<br \/>\nThe shape of the triangle = 324<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = (1\/2) x the product of the base b and the product of the height h<br \/>\narea = (1\/2) x b x h<br \/>\nSob = 36 cm , h =\u00a0 18 cm<br \/>\narea = (1\/2) x 648<br \/>\narea = 324 sq. cm<\/p>\n<p>Question 19.<\/p>\n<p><strong>FINDING A MISSING DIMENSION<\/strong><br \/>\n<strong>Find the missing dimension of the triangle.<\/strong><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-72.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 72\" width=\"161\" height=\"144\" \/><\/p>\n<p>So base = 7 m<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-73.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 73\" width=\"172\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\nBase of the triangle = 4.66 ft<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle =(1\/2) x\u00a0 the product of the base b and the product of height h<br \/>\narea of the triangle = 14 ft given<br \/>\nSo the height = 6 ft given<br \/>\narea =\u00a0 (1\/2) x b x h<br \/>\narea = (1\/2) x 4.66 x 6<br \/>\narea = (1\/2) x 27.96<br \/>\narea = 14<br \/>\nsoo base = 4.66 ft<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-74.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 74\" width=\"110\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nHeight = 2.66 in<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) x the product of the base and the product of the height<br \/>\narea = (1\/2) x 1.5 x h given that area = 2 in<br \/>\n2 = (1\/2) x 1.5h<br \/>\n1.5 h = 4<br \/>\nh = (4\/1.5)<br \/>\nh = 2.66 in<br \/>\n<strong>COMPOSITE FIGURES<\/strong><br \/>\n<strong>Find the area of the \ufb01gure.<\/strong><\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-75.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 75\" width=\"154\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the figure = 44 ft<\/p>\n<p>Explanation:<br \/>\nThe area of the rectangle = 2 x(length + breadth)<br \/>\narea = 2 x (12 +10)<br \/>\narea = 2 x (22)<br \/>\narea = 44 sq. ft<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-76.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 76\" width=\"180\" height=\"162\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the figure = 52 cm<\/p>\n<p>Explanation:<br \/>\nThe area of the rectangle = 2 x(length + breadth)<br \/>\narea = 2 x (11 +15)<br \/>\narea = 2 x (26)<br \/>\narea = 52 cm<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-77.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 77\" width=\"165\" height=\"197\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the perimeter = 5\/2 x a x b<\/p>\n<p>Explanation:<br \/>\nThe area of the perimeter = (5\/2) x a x b<br \/>\nwhere a = middle point<br \/>\nb = sides<\/p>\n<p>Question 26.<br \/>\n<strong>WRITING<\/strong><br \/>\nYou know the height and the perimeter of an equilateral triangle. Explain how to \ufb01nd the area of the triangle. Draw a diagram to support your reasoning.<img loading=\"lazy\" class=\"alignnone size-medium wp-image-31262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-30-300x297.png\" alt=\"\" width=\"300\" height=\"297\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-30-300x297.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-30-150x150.png 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-30.png 303w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Answer:<br \/>\nThe perimeter of the equilateral triangle = a\u00a0 x a x a = 3a<\/p>\n<p>Explanation:<br \/>\nThe perimeter of the equilateral triangle = 3a<br \/>\nheight of the equilateral triangle = h<br \/>\nthe area of the triangle = (1\/2) x product of base b and the product of the height h<br \/>\narea = (1\/2) x bh<\/p>\n<p>Question 27.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe total area of the polygon is 176 square feet. What is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-78.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 78\" width=\"268\" height=\"123\" \/><\/p>\n<p>Answer:<br \/>\nThe value of x = 6<\/p>\n<p>Explanation:<br \/>\nThe area of the polygon = 176 square feet given<br \/>\narea = 16 x 8 = 128<br \/>\narea = 176 &#8211; 128 = 48<br \/>\nThe area of the right angle triangle = (a x b )\/2<br \/>\narea = (8 x X)\/2<br \/>\n48 = 4x + 4x<br \/>\n8x = 48<br \/>\nx = (48\/8)<br \/>\nx = 6 ft<\/p>\n<p>Question 28.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe base and the height of Triangle A are one-half the base and the height of Triangle B. How many times greater is the area of Triangle B?<\/p>\n<p>Answer:<br \/>\n2 times<\/p>\n<p>Explanation:<br \/>\nThe triangle B is 2 times greater than the triangle A<\/p>\n<p>Question 29.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nUse what you know about \ufb01nding areas of triangles to write a formula for the area of a rhombus in terms of its diagonals. Compare the formula with your answer to Section 7.1 Exercise 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-79.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 79\" width=\"153\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = (1\/2) ab<br \/>\nThe area of the rhombus = (1\/2) ab<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle is equal to the area of the rhombus<br \/>\narea of the triangle = (1\/2) ab<br \/>\narea of the rhombus = (1\/2) ab<\/p>\n<h3><a id=\"Lesson_7.3_Areas_of_Trapezoids_and_Kites\"><\/a>Lesson 7.3 Areas of Trapezoids and Kites<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Deriving the Area Formula of a Trapezoid<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Draw any parallelogram on a piece of centimeter grid paper. Cut the parallelogram into two identical trapezoids. How can you use the area of the parallelogram to \ufb01nd the area of each trapezoid?<br \/>\nb. Copy the trapezoid below on a piece of centimeter grid paper. Find the area of the trapezoid. Explain how you found the area.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-80.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 80\" width=\"511\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-80.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-80-300x154.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><br \/>\nc. Draw any trapezoid on a piece of centimeter grid paper and \ufb01nd its area.<br \/>\nd. Use your results to write a formula for the area A of a trapezoid. Use the formula to \ufb01nd the area of the trapezoid shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-81.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 81\" width=\"155\" height=\"161\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-82.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 82\" width=\"158\" height=\"264\" \/><\/p>\n<p><strong>7.3 Lesson<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-83.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 83\" width=\"202\" height=\"72\" \/><br \/>\nYou can use decomposition to \ufb01nd areas of trapezoids and kites. A kite is a quadrilateral that has two pairs of adjacent sides with the same length and opposite sides with different lengths.<\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Find the area of the \ufb01gure.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-87.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 87\" width=\"190\" height=\"171\" \/><\/p>\n<p>Answer:<br \/>\n76.5 in<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (5 + 12). Given that b1 = 5 and b2 = 12<br \/>\narea = (1\/2) x 9(17) given that h = 9<br \/>\narea = (1\/2) x 153<br \/>\narea = 76.5 sq. in<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-88.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 88\" width=\"159\" height=\"199\" \/><\/p>\n<p>Answer:<br \/>\n65.45 sq. mi<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (3 + 3). Given that b1 = 3 and b2 = 3<br \/>\narea = (1\/2) x 7.7(17) given that h = 7.7<br \/>\narea = (1\/2) x 130.9<br \/>\narea = 65.45 sq. mi<\/p>\n<p>In Example 1(a), you could have used a copy of the trapezoid to form a parallelogram. As you may have discovered in the exploration, this leads to the following formula for the area of a trapezoid.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-89.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 89\" width=\"537\" height=\"229\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-89.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-89-300x128.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Find the area of the trapezoid.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-90.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 90\" width=\"172\" height=\"161\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 22.5 sq. mm<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (5 + 4). Given that b1 = 5 and b2 = 4<br \/>\narea = (1\/2) x 8(9) given that h = 8<br \/>\narea = (1\/2) x 45<br \/>\narea = 22.5 sq. mm<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-91.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 91\" width=\"145\" height=\"159\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 30 sq. in<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (7.7 + 2.3). Given that b1 = 7.7 and b2 = 2.3<br \/>\narea = (1\/2) x 6(10) given that h = 6 in<br \/>\narea = (1\/2) x 60<br \/>\narea = 30 sq. in<\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Find the area of the \ufb01gure.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-92.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 92\" width=\"197\" height=\"153\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid1 = 60 sq. m<br \/>\nThe area of the trapezoid2= 88 sq. m<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid1 = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (5 + 5). Given that b1 = 5\u00a0 and b2 = 5<br \/>\narea = (1\/2) x 12(10) given that h = 6 m<br \/>\narea = (1\/2) x\u00a0 120<br \/>\narea = 60 sq. m<br \/>\nThe area of the trapezoid2 = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (8 + 8). Given that b1 = 8\u00a0 and b2 = 8<br \/>\narea = (1\/2) x 11(16) given that h = 6 m<br \/>\narea = 88 sq. m<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-93.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 93\" width=\"162\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 112 sq. in<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (6+ 10). Given that b1 = 6 and b2 = 10<br \/>\narea = (1\/2) x 14(16) given that h = 14 in<br \/>\narea = (1\/2) x 224<br \/>\narea = 112 sq. in<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\n<strong>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/strong><\/p>\n<p>Question 7.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to use the area of a parallelogram to \ufb01nd the area of a trapezoid.<\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = product of the height h and the product of the base b<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<\/p>\n<p>Question 8.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhat measures do you need to \ufb01nd the area of a kite?<\/p>\n<p>Answer:<br \/>\nRhombus is used to find the area of the kite<\/p>\n<p>Explanation:<br \/>\nThe area of the rhombus = (1\/2) x side x height<br \/>\narea = (1\/2) x s x h<br \/>\narea = (1\/2) sh<br \/>\nkite is also same as the rhombus<\/p>\n<p><strong>FINDING AREA<\/strong><br \/>\n<strong>Find the area of the \ufb01gure.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-94.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 94\" width=\"215\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nArea = 52.5 sq. yd<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = (1\/2) x height x the product of the base 1 and the base 2<br \/>\narea = (1\/2) x height x (b1 + b2)<br \/>\narea = (1\/2) x 5 x (9 + 12)<br \/>\narea = (1\/2) x 5 x 21<br \/>\narea = (1\/2) x 105<br \/>\narea = 52.5 sq. yd<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-95.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 95\" width=\"145\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\nArea = 55 sq. m<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = (1\/2) x height x the product of the base 1 and the base 2<br \/>\narea = (1\/2) x height x (b1 + b2)<br \/>\narea = (1\/2) x 10 x (7 + 4)<br \/>\narea = (1\/2) x 10x 11<br \/>\narea = (1\/2) x 110<br \/>\narea = 55 sq. m<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAn archaeologist estimates that the manuscript shown was originally a rectangle with a length of 20 inches. Estimate the area of the fragment that is missing.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-96.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 96\" width=\"201\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\n144 square inches<\/p>\n<p>Explanation:<br \/>\nThe area of the right angle triangle = a x b where a = height b = base<br \/>\narea = a x b a=12 b = 18 &#8211; 6 = 12<br \/>\narea = 12 x 12<br \/>\narea = 144 sq. in<\/p>\n<p>Question 12.<br \/>\nThe stained-glass window is made of identical kite-shaped glass panes. The approximate dimensions of one pane are shown. The glass used to make the window costs $12.50 per square foot. Find the total cost of the glass used to make the window.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-97.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 97\" width=\"248\" height=\"194\" \/><\/p>\n<p>Answer:<br \/>\nThe total cost of the glass used to make the window is 14.4375 $<br \/>\nExplanation:<br \/>\nThe area of the rhombus = (1\/2) x the product of the side s and the product of height h<br \/>\narea\u00a0 = (1\/2) x2 ft x 2.31ft<br \/>\narea = ( 4.62\/2)<br \/>\nArea = 2.31 x 12.50$<br \/>\narea = 14.4375$<\/p>\n<h3><a id=\"Areas_of_Trapezoids_and_Kites_Homework_&amp;_Practice_7.3\"><\/a>Areas of Trapezoids and Kites Homework &amp; Practice 7.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the area of the triangle.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-98.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 98\" width=\"192\" height=\"103\" \/><\/p>\n<p>Answer:<br \/>\nArea =63 in<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = half the product of the base and the product of the height<br \/>\narea = (1\/2)bh<br \/>\narea = (1\/2) x 18 x 7<br \/>\narea = (126\/2)<br \/>\narea = 63 in<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-99.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 99\" width=\"158\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nArea =26 sq. km<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = half the product of the base and the product of the height<br \/>\narea = (1\/2)bh<br \/>\narea = (1\/2) x 8 x 6.5<br \/>\narea = (52\/2)<br \/>\narea = 26 sq. km<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-100.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 100\" width=\"235\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nArea =25 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = half the product of the base and the product of the height<br \/>\narea = (1\/2)bh<br \/>\narea = (1\/2) x 4 x 12.5<br \/>\narea = (50\/2)<br \/>\narea = 25 sq. ft<\/p>\n<p><strong>Classify the quadrilateral.\/<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-101.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 101\" width=\"149\" height=\"88\" \/><\/p>\n<p>Answer:<br \/>\nThe above quadrilateral look similar to the rectangle<\/p>\n<p>Explanation:<br \/>\nRectangle<br \/>\nthe area of the rectangle = length x width<br \/>\narea = l x w<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-102.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 102\" width=\"139\" height=\"84\" \/><\/p>\n<p>Answer:<br \/>\nThe above diagram is\u00a0 similar to the trapezoid<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = half the product of the base and the product of the height<br \/>\narea = (1\/2) x b x h<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-103.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 103\" width=\"141\" height=\"91\" \/><\/p>\n<p>Answer:<br \/>\nThe above figure is similar to the parallelogram<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the height and the product of the base b<br \/>\narea = b x h<\/p>\n<p>Question 7.<br \/>\nOn a normal day, 12 airplanes arrive at an airport every 15 minutes. Which rate does not represent this situation?<br \/>\nA. 24 airplanes every 30 minutes<br \/>\nB. 4 airplanes every 5 minutes<br \/>\nC. 6 airplanes every 5 minutes<br \/>\nD. 48 airplanes each hour<\/p>\n<p>Answer:<br \/>\nB<\/p>\n<p>Explanation:<br \/>\n4 airplanes every 5 minutes<br \/>\n<strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>USING TOOLS<\/strong><br \/>\n<strong>Find the area of the trapezoid by forming a parallelogram.<\/strong> (See Exploration 1, p. 297.)<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-104.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 104\" width=\"158\" height=\"100\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = (1\/2) x b x l x h<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = (1\/2) x b x l x h<br \/>\narea = (1\/2) x b x h x l<br \/>\narea = (lxb\/2)x h<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-105.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 105\" width=\"157\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = (1\/2) x b x l x h<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = (1\/2) x b x l x h<br \/>\narea = (1\/2) x b x h x l<br \/>\narea = (lxb\/2)x h<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-106.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 106\" width=\"160\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = (1\/2) x b x l x h<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = (1\/2) x b x l x h<br \/>\narea = (1\/2) x b x h x l<br \/>\narea = (lxb\/2)x h<\/p>\n<p><strong>FINDING AREA<\/strong><br \/>\n<strong>Use decomposition to \ufb01nd the area of the \ufb01gure.<\/strong><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-107.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 107\" width=\"130\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\n25 cm<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) b x h<br \/>\nbase value = 2, height = 5 given<br \/>\narea = (1\/2) x 5 x 2<br \/>\narea = 5<br \/>\nthe area of another triangle = 5<br \/>\nthe remaining = rectangle<br \/>\narea of rectangle = length x breadth<br \/>\narea = 15 + 5 + 5 = 25 cm<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-108.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 108\" width=\"154\" height=\"140\" \/><\/p>\n<p>Answer:<br \/>\n92 sq. yd<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) b x h<br \/>\nbase value = 2, height = 5 given<br \/>\narea = (1\/2) x 8 x 2=3<br \/>\narea = 12<br \/>\nthe remaining = rectangle<br \/>\narea of rectangle = length x breadth<br \/>\narea = 80 + 12 yd<br \/>\narea = 92 yd<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-109.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 109\" width=\"196\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\n125 m<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) b x h<br \/>\nbase value = 2, height = 5 given<br \/>\narea = (1\/2) x 8 x 5= 20<br \/>\narea = 20<br \/>\nThe area of the triangle = (1\/2) b x h<br \/>\nbase value = 17, height = 5 given<br \/>\narea = (1\/2) x 17 x 5= 20<br \/>\narea = 42.5<br \/>\narea\u00a0 = 20 + 20+ 42.5 + 42.5<br \/>\narea = 125 m<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-110.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 110\" width=\"129\" height=\"167\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the figure = 44 inches<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) b x h<br \/>\nbase value = 9, height = 4 given<br \/>\narea = (1\/2) x 9 x 4= 18<br \/>\narea = 18<br \/>\nthe remaining = rectangle<br \/>\narea of rectangle = length x breadth<br \/>\narea = 18 + 18 + 4 +<br \/>\narea = 44 inches<br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-111.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 111\" width=\"195\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the figure = 55\u00a0 miles<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) b x h<br \/>\nbase value = 10, height = 7 given<br \/>\narea = (1\/2) x 10 x 7= 35<br \/>\narea = 35 mi<br \/>\nThe area of the triangle = (1\/2) b x h<br \/>\nbase value = 10, height = 4 given<br \/>\narea = (1\/2) x 10 x 4= 20<br \/>\narea = 20 mi<br \/>\narea =\u00a0 20 + 35 = 55<br \/>\narea = 55 mi<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-112.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 112\" width=\"168\" height=\"150\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the figure = 17.68 miles<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2) b x h<br \/>\nbase value = 3.2, height = 3.8 given<br \/>\narea = (1\/2) x 3.2 x 3.8= 35<br \/>\narea = 6.08<br \/>\nThe area of the triangle = (1\/2) b x h<br \/>\nbase value = 3.2, height = 1.6given<br \/>\narea = (1\/2) x 3.2 x 1.6= 20<br \/>\narea = 2.56<br \/>\narea =\u00a0 2.56 + 2.56 + 6.08 + 6.08 = 17.68 kms<br \/>\narea = 17.68 miles<\/p>\n<p><strong>FINDING AREA<\/strong><br \/>\n<strong>Find the area of the trapezoid.<\/strong><\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-113.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 113\" width=\"160\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\n28 in<\/p>\n<p>Explanation:<br \/>\nArea of trapezoid = half the product of the height and the product\u00a0 of the bases<br \/>\narea = (1\/2) x h x (b1 +b2)<br \/>\narea = (1\/2) x 4 x\u00a0 (6 + 8)\/<br \/>\narea = (1\/2) x 4 x 14<br \/>\narea = 28 sq. in<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-114.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 114\" width=\"132\" height=\"151\" \/><\/p>\n<p>Answer:<br \/>\n10 sq. cm<\/p>\n<p>Explanation:<br \/>\nArea of trapezoid = half the product of the height and the product\u00a0 of the bases<br \/>\narea = (1\/2) x h x (b1 +b2)<br \/>\narea = (1\/2) x 4 x\u00a0 (3.5 + 1.5)<br \/>\narea = (1\/2) x 4 x 5<br \/>\narea = 10 sq. cm<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-115.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 115\" width=\"191\" height=\"156\" \/><\/p>\n<p>Answer:<br \/>\n105 sq. ft<\/p>\n<p>Explanation:<br \/>\nArea of trapezoid = half the product of the height and the product\u00a0 of the bases<br \/>\narea = (1\/2) x h x (b1 +b2)<br \/>\narea = (1\/2) x 10 x\u00a0 (13.5 + 7.5)<br \/>\narea = (1\/2) x 10 x 21<br \/>\narea = 105 sq. ft<\/p>\n<p>Question 20.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the area of the trapezoid. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-116.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 116\" width=\"315\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-116.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-116-300x152.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/p>\n<p>Answer:<br \/>\nNo my friend is not correct<\/p>\n<p>Explanation:<br \/>\nArea of trapezoid = half the product of the height and the product\u00a0 of the bases<br \/>\narea = (1\/2) x h x (b1 +b2)<br \/>\narea = (1\/2) x 8 x\u00a0 (6 +14)<br \/>\narea = (1\/2) x 160<br \/>\narea = 80 sq. m<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nLight shines through a window. What is the area of the trapezoid-shaped region created by the light?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-117.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 117\" width=\"198\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\n16 sq. ft<br \/>\nExplanation:<br \/>\nArea of trapezoid = half the product of the height and the product\u00a0 of the bases<br \/>\narea = (1\/2) x h x (b1 +b2) given that b1 = 3 and b2 = 5<br \/>\narea = (1\/2) x 4 x\u00a0 (5 +3)<br \/>\narea = (1\/2) x 32<br \/>\narea = 16 sq. ft<\/p>\n<p><strong>COMPOSITE FIGURES<\/strong><br \/>\n<strong>Find the area of the \ufb01gure.<\/strong><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-118.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 118\" width=\"189\" height=\"193\" \/><\/p>\n<p>Answer:<br \/>\n178.5 sq. ft<br \/>\nExplanation:<br \/>\nArea of trapezoid = half the product of the height and the product\u00a0 of the bases<br \/>\narea = (1\/2) x h x (14 +7) given that b1 = 14 and b2 = 7<br \/>\narea = (1\/2) x 17 x\u00a0 (14 +7)<br \/>\narea = (1\/2) x 357<br \/>\narea = 178.5 sq. ft<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-119.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 119\" width=\"160\" height=\"194\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-120.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 120\" width=\"155\" height=\"191\" \/><\/p>\n<p><strong>FINDING A MISSING DIMENSION<\/strong><br \/>\n<strong>Find the height of the trapezoid.<\/strong><\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-121.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 121\" width=\"125\" height=\"194\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the trapezoid = square root of height and bases<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-122.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 122\" width=\"137\" height=\"191\" \/><\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-123.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 123\" width=\"181\" height=\"195\" \/><\/p>\n<p><strong>FINDING AREA<\/strong><br \/>\n<strong>Find the area (in square feet) of a trapezoid with height hand bases b<sub>1<\/sub> and b<sub>2<\/sub>.<\/strong><\/p>\n<p>Question 28.<br \/>\nh = 6 in.<br \/>\nb<sub>1<\/sub> = 9 in.<br \/>\nb<sub>2<\/sub> = 12 in.<\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 0.43722 square feet<\/p>\n<p>Explanation:<br \/>\nArea of trapezoid = half the product of the height and the product\u00a0 of the bases<br \/>\narea = (1\/2) x h x (9 +12) given that b1 = 9 and b2 = 12<br \/>\narea = (1\/2) x 6 x\u00a0 (9 + 12)<br \/>\narea = (1\/2) x 126<br \/>\narea = 63 in<br \/>\n1 inch = 0.00694 sq feet<br \/>\nso 0.43722sq ft<\/p>\n<p>Question 29.<br \/>\nh = 12 yd<br \/>\nb<sub>1<\/sub> = 5 yd<br \/>\nb<sub>2<\/sub> = 7 yd<\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 648 square feet<\/p>\n<p>Explanation:<br \/>\nArea of trapezoid = half the product of the height and the product\u00a0 of the bases<br \/>\narea = (1\/2) x h x (5 +7) given that b1 = 5 and b2 = 7<br \/>\narea = (1\/2) x 12 x\u00a0 (5 + 7)<br \/>\narea = (1\/2) x 144<br \/>\narea =72 yd<br \/>\n1 yard = 9 sq feet<br \/>\nso 72 yd = 72 x 9 sq ft<br \/>\narea = 648 sq ft<\/p>\n<p>Question 30.<br \/>\nh = 6 m<br \/>\nb<sub>1<\/sub> = 3 m<br \/>\nb<sub>2<\/sub> = 8 m<\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 355.212 square feet<\/p>\n<p>Explanation:<br \/>\nArea of trapezoid = half the product of the height and the product\u00a0 of the bases<br \/>\narea = (1\/2) x h x (3 +8) given that b1 = 3 and b2 = 8<br \/>\narea = (1\/2) x 6 x\u00a0 (3 + 8)<br \/>\narea = (1\/2) x 66<br \/>\narea =33 m<br \/>\n1 m\u00a0 = 10.764 sq feet<br \/>\nso 33 m = 33 x 10.764sq ft<br \/>\narea = 355.212 sq ft<\/p>\n<p>Question 31.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nThe area of the trapezoidal student election sign is 5 square feet. Find two possible values for each base length.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-123.1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 123.1\" width=\"279\" height=\"377\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-123.1.png 279w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-123.1-222x300.png 222w\" sizes=\"(max-width: 279px) 100vw, 279px\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 4 ft<\/p>\n<p>Explanation:<br \/>\nArea of trapezoid = half the product of the height and the product\u00a0 of the bases<br \/>\narea = (1\/2) x h x (4 +4) given that b1 = 4 and b2 = 4<br \/>\narea = (1\/2) x 2 x\u00a0 (4 + 4)<br \/>\narea = (1\/2) x 8<br \/>\narea = 4 sq. ft<\/p>\n<p>Question 32.<br \/>\n<strong>REASONING<\/strong><br \/>\nHow many times greater is the area of the \ufb02oor covered by the larger speaker than by the smaller speaker?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-124.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 124\" width=\"335\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-124.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-124-300x234.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/p>\n<p>Answer:<br \/>\n2 times<\/p>\n<p>Explanation:<br \/>\nThe larger speaker is 2 times greater than that of the smaller speaker<\/p>\n<p>Question 33.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe rectangle and the trapezoid have the same area. What is the length \u2113 of the rectangle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-125.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 125\" width=\"328\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-125.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-125-300x98.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Question 34.<\/p>\n<p>Answer:<br \/>\nThe area of the triangle =36<br \/>\nExplanation:<br \/>\nIn the above given trapezoid the bases b1 = 12 and b2 = 24 height = 9 ft<br \/>\nSo the area of the trapezoid = (1\/2) x h x(b1 + b2)<br \/>\narea = (1\/2) x 9 x (12 +24)<br \/>\narea = (1\/2) x 324<br \/>\narea = 162<br \/>\nThe length of the triangle = length X w<br \/>\n162 = 9l<br \/>\nlength = 36 ft<\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\nIn the \ufb01gureshown, the area of the trapezoid is less than twice the area of the triangle. Find the possible values of x. Can the trapezoid have the same area as the triangle? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-126.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 126\" width=\"175\" height=\"161\" \/><\/p>\n<p>Answer:<br \/>\nThe possible value of x = 15 in<\/p>\n<p>Explanation:<br \/>\nIn the above statement they said that the area of the trapezoid is less than twice the area of the triangle<br \/>\narea of the triangle = (1\/2) x b x h<br \/>\narea = (1\/2)\u00a0 x 15 x 10<br \/>\narea = (150\/2) =75<br \/>\nArea of trapezoid = (1\/2) x h x (b1 + b2)<br \/>\narea = (1\/2) x 10 x (15 +15)<br \/>\narea = (300\/2)<br \/>\narea = 150<br \/>\nSo the area of the trapezoid is 2 times less than the area of the triangle.<\/p>\n<p>Question 35.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nIn Section 7.1 Exercise 34 and Section 7.2 Exercise 29, you wrote a formula for the area of a rhombus in terms of its diagonals.<br \/>\na. Use what you know about \ufb01nding areas of \ufb01gures to write a formula for the area of a kite in terms of its diagonals.<br \/>\nb. Are there any similarities between your formula in part(a) and the formula you found in Sections 7.1 and 7.2? Explain why or why not.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-127.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 127\" width=\"156\" height=\"206\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the rhombus = (1\/2) x side x height<\/p>\n<p>Explanation:<br \/>\nThe kite is looking the same as the rhombus<br \/>\narea of the rhombus = (1\/2) x side x height<\/p>\n<h3><a id=\"Lesson_7.4_Three_Dimensional_Figures\"><\/a>Lesson 7.4 Three-Dimensional Figures<\/h3>\n<p><strong>EXPLORATION 1<br \/>\nExploring Faces, Edges and Vertices<\/strong><br \/>\n<strong>Work with a partner. Use the rectangular prism shown.<\/strong><br \/>\na. Prisms have faces, edges, and vertices. What does each of these terms mean?<br \/>\nb. What does it mean for lines or planes to be parallel or perpendicular in three dimensions? Use drawings to identify one pair of each of the following.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-128.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 128\" width=\"154\" height=\"115\" \/><\/p>\n<ul>\n<li>parallel faces<\/li>\n<li>parallel edges<\/li>\n<li>edge parallel to a face<\/li>\n<li>perpendicular faces<\/li>\n<li>perpendicular edges<\/li>\n<li>edge perpendicular to a face<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-26037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-128.1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 128.1\" width=\"156\" height=\"188\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p><strong>Drawing Views of a Solid<\/strong><br \/>\n<strong>Work with a partner. Draw the front, side, and top views of each stack of cubes. Then \ufb01nd the number of cubes in the stack. An example is shown at the left.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-129.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 129\" width=\"204\" height=\"219\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-129.1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 129.1\" width=\"414\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-129.1.png 414w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-129.1-300x214.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><\/p>\n<p>Answer:<br \/>\na: the number of cubes = 4<br \/>\nb: the number of cubes = 4<br \/>\nc: the number of cubes = 5<br \/>\nd: the number of cubes = 6<\/p>\n<p>Explanation:<br \/>\na:<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-40-300x50.png\" alt=\"\" width=\"300\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-40-300x50.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-40-768x127.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-40.png 800w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb::<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-40-300x50.png\" alt=\"\" width=\"300\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-40-300x50.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-40-768x127.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-40.png 800w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nc:<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32471\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-44-300x52.png\" alt=\"\" width=\"300\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-44-300x52.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-44-768x132.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-44.png 803w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nd:<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32472\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-45-300x50.png\" alt=\"\" width=\"300\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-45-300x50.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-45-768x127.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-45.png 799w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>7.4 Lesson<\/strong><\/p>\n<p>A solid is a three-dimensional \ufb01gure that encloses a space. A polyhedron is a solid whose faces are all polygons.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-130.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 130\" width=\"491\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-130.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-130-300x100.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the numbers of faces, edges, and vertices of the solid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-131.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 131\" width=\"143\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nfaces = 5<br \/>\nedges = 12<br \/>\nvertices = 6<\/p>\n<p>Explanation:<br \/>\nThe number of faces = 5<br \/>\nthe number of edges = 12<br \/>\nthe number of vertices = 6<\/p>\n<p><strong>Key Ideas<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-26044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-132.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 132\" width=\"491\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-132.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-132-300x178.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Draw the solid.<\/strong><\/p>\n<p>Question 2.<br \/>\nsquare prism<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-37.png\" alt=\"\" width=\"170\" height=\"203\" \/><\/p>\n<p>Question 3.<br \/>\npentagonal pyramid<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-38.png\" alt=\"\" width=\"188\" height=\"220\" \/><\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-26043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-132.1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 132.1\" width=\"146\" height=\"147\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>FACES, EDGES, AND VERTICES<\/strong><br \/>\nFind the numbers of faces, edges, and vertices of the solid at the left.<\/p>\n<p>Answer:<br \/>\nfaces : 3<br \/>\nedges : 6<br \/>\nvertices : 3<\/p>\n<p>Explanation:<br \/>\nThe number of faces of solid at the left = 3<br \/>\nedges = 6<br \/>\nvertices = 3<\/p>\n<p>Question 5.<br \/>\n<strong>DRAWING A SOLID<\/strong><br \/>\nDraw an octagonal prism.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-39.png\" alt=\"\" width=\"171\" height=\"169\" \/><\/p>\n<p>Question 6.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich \ufb01guredoes not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-133.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 133\" width=\"490\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-133.png 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-133-300x76.png 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/p>\n<p>Answer:<br \/>\nThe 3rd figure is different from the other 3 figures<\/p>\n<p>Explanation:<br \/>\nThe 3rd figure is the same as the square prism<br \/>\nthe other 3 figures are triangular prisms<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\nThe Flatiron Building in New York City is in the shape of a triangular prism. Draw a sketch of the building.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-134.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 134\" width=\"187\" height=\"268\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32526\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-68.png\" alt=\"\" width=\"268\" height=\"180\" \/><\/p>\n<p>Question 8.<br \/>\nThe Pyramid of the Niches is in El Taj\u00edn, an archaeological site in Veracruz, Mexico. Draw the front, side, and top views of the pyramid. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-135.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 135\" width=\"225\" height=\"179\" \/><\/p>\n<p>Answer:<br \/>\nFront = 2<br \/>\nside = 1<br \/>\ntop = 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32525\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-67-300x55.png\" alt=\"\" width=\"300\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-67-300x55.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-67-768x141.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-67.png 795w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 9.<br \/>\nUse the point-cut diamond shown.<br \/>\na. Find the numbers of faces, edges, and vertices of the diamond.<br \/>\nb. Draw the front, side, and top views of the diamond.<br \/>\nc. How can a jeweler transform the point-cut diamond into a table-cut diamond as in Example 3?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-136.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 136\" width=\"144\" height=\"162\" \/><\/p>\n<p>Answer:<br \/>\na : the number of faces = 8,edges = 16,vertices = 6<br \/>\nb : front = 2 , side = 2,top = 1<\/p>\n<p>Explanation:<br \/>\na : faces = 8<br \/>\nedges = 16<br \/>\nvertices = 6<br \/>\nb : <img loading=\"lazy\" class=\"alignnone size-medium wp-image-32522\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-66-300x48.png\" alt=\"\" width=\"300\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-66-300x48.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-66-768x122.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-66.png 819w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h3><a id=\"Three_Dimensional_Figures_Homework_&amp;_Practice_7.4\"><\/a>Three-Dimensional Figures Homework &amp; Practice 7.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the area of the \ufb01gure.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-137.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 137\" width=\"146\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 15 ft<br \/>\nExplanation:<br \/>\nIn the above given trapezoid the bases b1 = 12 and b2 = 24 height = 9 ft<br \/>\nSo the area of the trapezoid = (1\/2) x h x(b1 + b2)<br \/>\narea = (1\/2) x 3 x (4 +6)<br \/>\narea = (1\/2) x 30<br \/>\narea = 15<br \/>\nQuestion 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-138.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 138\" width=\"185\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 18 km<br \/>\nExplanation:<br \/>\nIn the above given trapezoid the bases b1 = 12 and b2 = 24 height = 9 ft<br \/>\nSo the area of the trapezoid = (1\/2) x h x(b1 + b2)<br \/>\narea = (1\/2) x 3 x (5 +7)<br \/>\narea = (1\/2) x 36<br \/>\narea = 18 km<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-139.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 139\" width=\"168\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 18 km<br \/>\nExplanation:<br \/>\nIn the above given trapezoid the bases b1 = 12 and b2 = 24 height = 9 ft<br \/>\nSo the area of the trapezoid = (1\/2) x h x(b1 + b2)<br \/>\narea = (1\/2) x 18 x (6 +6)<br \/>\narea = (1\/2) x 216<br \/>\narea = 18 k<\/p>\n<p><strong>Find the LCM of the numbers.<\/strong><\/p>\n<p>Question 4.<br \/>\n8, 12<\/p>\n<p>Answer:<br \/>\n24<\/p>\n<p>Explanation:<br \/>\nFactors of 8 = 2 x 2 x2<br \/>\nfactors of 12 = 2 x 2x 3<br \/>\nl.c.m. = 2 x 2 x 2x 3<br \/>\nl.c.m = 24<\/p>\n<p>Question 5.<br \/>\n15, 25<\/p>\n<p>Answer:<br \/>\n75<\/p>\n<p>Explanation:<br \/>\nFactors of 15 = 5 x 3<br \/>\nfactors of 25 = 5 x 5<br \/>\nl.c.m. = 5 x 3 x5<br \/>\nl.c.m = 75<\/p>\n<p>Question 6.<br \/>\n32, 44<\/p>\n<p>Answer:<br \/>\n352<\/p>\n<p>Explanation:<br \/>\nFactors of 32 = 8 x 4<br \/>\nfactors of 44 = 11 x 4<br \/>\nl.c.m. = 4 x 11 x 8<br \/>\nl.c.m = 352<\/p>\n<p>Question 7.<br \/>\n3, 7, 10<\/p>\n<p>Answer:<br \/>\n210<\/p>\n<p>Explanation:<br \/>\nFactors of 3 = 3 x 1<br \/>\nfactors of 7 = 7 x 1<br \/>\nfactors of 10 =5 x 2<br \/>\nl.c.m. = 3 x 7 x 5 x 2<br \/>\nl.c.m = 210<\/p>\n<p><strong>A bucket contains stones and seashells. You are given the number of seashells in the bucket and the ratio of stones to seashells. Find the number of stones in the bucket.<\/strong><\/p>\n<p>Question 8.<br \/>\n18 seashells; 2 to 1<\/p>\n<p>Answer:<br \/>\nNo of stones = 12<br \/>\nNo of seashells = 6<\/p>\n<p>Explanation:<br \/>\n(18\/3) = 6<br \/>\n2 : 1 = 12 : 6<\/p>\n<p>Question 9.<br \/>\n30 seashells; 4 : 3<\/p>\n<p>Answer:<br \/>\nNo of stones = 17.14<br \/>\nNo of seashells = 12.6<\/p>\n<p>Explanation:<br \/>\n(30\/7) = 4.2<br \/>\n4 : 3 = 17.4 : 12.6<\/p>\n<p>Question 10.<br \/>\n40 seashells; 7 : 4<\/p>\n<p>Answer:<br \/>\nNo of stones = 25.45<br \/>\nNo of seashells = 14.54<\/p>\n<p>Explanation:<br \/>\n(40\/11) = 3.63<br \/>\n7 : 4 = 25.45 : 14.54<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>DRAWING VIEWS OF A SOLID<\/strong><br \/>\n<strong>Draw the front, side, and top views of the stack of cubes. Then \ufb01nd the number of cubes in the stack.<\/strong> (See Exploration 2, p. 305.)<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-140.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 140\" width=\"106\" height=\"78\" \/><\/p>\n<p>Answer:<br \/>\nfront = 10<br \/>\nside = 3<br \/>\ntop = 4<\/p>\n<p>Explanation:<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32475\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-48-300x56.png\" alt=\"\" width=\"300\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-48-300x56.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-48-768x143.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-48.png 798w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-141.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 141\" width=\"125\" height=\"79\" \/><\/p>\n<p>Answer:<br \/>\nfront = 9<br \/>\nside = 3<br \/>\ntop = 5<\/p>\n<p>Explanation:<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-47-300x57.png\" alt=\"\" width=\"300\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-47-300x57.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-47-768x147.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-47.png 809w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-142.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 142\" width=\"110\" height=\"87\" \/><\/p>\n<p>Answer:<br \/>\nfront = 5<br \/>\nside = 5<br \/>\ntop = 8<\/p>\n<p>Explanation:<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32473\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-46-300x54.png\" alt=\"\" width=\"300\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-46-300x54.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-46-768x137.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-46.png 818w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>FACES, EDGES, AND VERTICES<\/strong><br \/>\n<strong>Find the numbers of faces, edges, and vertices of the solid.<\/strong><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-143.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 143\" width=\"81\" height=\"106\" \/><\/p>\n<p>Answer:<br \/>\nfaces = 10<br \/>\nedges = 24<br \/>\nvertices = 9<\/p>\n<p>Explanation:<br \/>\nThe number of faces = 10<br \/>\nthe number of edges = 24<br \/>\nthe number of vertices =9<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-144.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 144\" width=\"127\" height=\"106\" \/><\/p>\n<p>Answer:<br \/>\nfaces = 17<br \/>\nedges = 34<br \/>\nvertices = 13<\/p>\n<p>Explanation:<br \/>\nThe number of faces = 17<br \/>\nthe number of edges = 34<br \/>\nthe number of vertices =13<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-145.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 145\" width=\"159\" height=\"87\" \/><\/p>\n<p>Answer:<br \/>\nfaces = 10<br \/>\nedges = 20<br \/>\nvertices = 7<\/p>\n<p>Explanation:<br \/>\nThe number of faces = 10<br \/>\nthe number of edges = 20<br \/>\nthe number of vertices =7<\/p>\n<p><strong>DRAWING SOLIDS<\/strong><br \/>\n<strong>Draw the solid.<\/strong><\/p>\n<p>Question 17.<br \/>\ntriangular prism<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-33.png\" alt=\"\" width=\"240\" height=\"134\" \/><\/p>\n<p>Question 18.<br \/>\npentagonal prism<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-34.png\" alt=\"\" width=\"238\" height=\"233\" \/><\/p>\n<p>Question 19.<br \/>\nrectangular pyramid<img loading=\"lazy\" class=\"alignnone size-full wp-image-32289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-35.png\" alt=\"\" width=\"236\" height=\"215\" \/><\/p>\n<p>Question 20.<br \/>\nhexagonal pyramid<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-36.png\" alt=\"\" width=\"189\" height=\"208\" \/><\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe Pyramid of Cestius in Rome, Italy, is in the shape of a square pyramid. Draw a sketch of the pyramid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-146.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 146\" width=\"235\" height=\"174\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32516\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-65.png\" alt=\"\" width=\"226\" height=\"192\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>RESEARCH<\/strong><br \/>\nUse the Internet to \ufb01nd a picture of the Washington Monument. Describe its shape.<\/p>\n<p><strong>DRAWING VIEWS OF A SOLID<\/strong><br \/>\n<strong>Draw the front, side, and top views of the solid.<\/strong><\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-147.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 147\" width=\"145\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\nfront = 1<br \/>\nside = 2<br \/>\ntop = 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32498\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-59-300x60.png\" alt=\"\" width=\"300\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-59-300x60.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-59-768x153.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-59.png 793w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-148.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 148\" width=\"135\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\nfront =2<br \/>\nside = 2<br \/>\ntop = 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32499\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-60-300x66.png\" alt=\"\" width=\"300\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-60-300x66.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-60-768x169.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-60.png 807w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-149.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 149\" width=\"132\" height=\"127\" \/><\/p>\n<p>Answer:<br \/>\nfront =2<br \/>\nside = 2<br \/>\ntop = 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32499\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-60-300x66.png\" alt=\"\" width=\"300\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-60-300x66.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-60-768x169.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-60.png 807w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-150.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 150\" width=\"138\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nfront =2<br \/>\nside = 2<br \/>\ntop = 2<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32509\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-61-300x56.png\" alt=\"\" width=\"300\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-61-300x56.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-61-768x143.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-61.png 818w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-151.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 151\" width=\"155\" height=\"123\" \/><\/p>\n<p>Answer:<br \/>\nfront = 1<br \/>\nside = 2<br \/>\ntop = 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32511\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-62-300x54.png\" alt=\"\" width=\"300\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-62-300x54.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-62-768x137.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-62.png 806w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-152.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 152\" width=\"161\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nfront = 1<br \/>\nside = 1<br \/>\ntop = 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32513\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-63-300x54.png\" alt=\"\" width=\"300\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-63-300x54.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-63-768x137.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-63.png 813w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>DRAWING SOLIDS<\/strong><br \/>\n<strong>Draw a solid with the following front, side, and top views.<\/strong><\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-153.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 153\" width=\"245\" height=\"86\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32514\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-64-300x226.png\" alt=\"\" width=\"300\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-64-300x226.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-64.png 330w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nfront = 2 top = 1 side = 2<\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-154.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 154\" width=\"244\" height=\"115\" \/><\/p>\n<p>Question 31.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nDesign and draw a house. Name the different solids that you can use to make a model of the house.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-155.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 155\" width=\"579\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-155.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-155-300x92.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTwo of the three views of a solid are shown.<br \/>\na. What is the greatest number of cubes in the solid?<br \/>\nb. What is the least number of cubes in the solid?<br \/>\nc. Draw the front views of both solids in parts (a) and (b).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-156.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 156\" width=\"169\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\na: The greatest number of cubes in the solid = 3<br \/>\nb : The least number of cubes in the solid = 2<br \/>\nc : <img loading=\"lazy\" class=\"alignnone size-medium wp-image-32477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-49-300x53.png\" alt=\"\" width=\"300\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-49-300x53.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-49-768x135.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-49.png 812w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 33.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nDraw two different solids with \ufb01ve faces.<br \/>\na. Write the numbers of vertices and edges for each solid.<br \/>\nb. Explain how knowing the numbers of edges and vertices helps you draw a three-dimensional \ufb01gure.<\/p>\n<p>Question 34.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe base of a pyramid has n sides. Find the numbers of faces, edges, and vertices of the pyramid. Explain your reasoning.<\/p>\n<h3><a id=\"Lesson_7.5_Surface_Areas_of_Prisms\"><\/a>Lesson 7.5 Surface Areas of Prisms<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Using Grid Paper to Construct a Solid<\/strong><br \/>\n<strong>Work with a partner. Copy the \ufb01gure shown below onto grid paper.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-157.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 157\" width=\"549\" height=\"264\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-157.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-157-300x144.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><br \/>\na. Cut out and fold the \ufb01gure to form a solid. What type of solid does the \ufb01gure form?<br \/>\nb. What is the area of the entire surface of the solid?<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Finding the Area of the Entire Surface<\/strong><br \/>\n<strong>Work with a partner. Find the area of the entire surface of each solid. Explain your reasoning.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-158.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 158\" width=\"383\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-158.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-158-300x114.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n<p>Answer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-26071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-159.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 159\" width=\"156\" height=\"173\" \/><\/p>\n<p><strong>7.5 Lesson<\/strong><\/p>\n<p>The surface area of a solid is the sum of the areas of all of its faces. You can use a two-dimensional representation of a solid, called a net, to \ufb01nd the surface area of the solid. Surface area is measured in square units.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-160.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 160\" width=\"199\" height=\"90\" \/><\/p>\n<p><strong>Key Idea<\/strong><br \/>\n<strong>Net of a Rectangular Prism<\/strong><br \/>\nA rectangular prism is a prism with rectangular bases.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-161.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 161\" width=\"566\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-161.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-161-300x98.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the surface area of the rectangular prism.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-162.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 162\" width=\"184\" height=\"106\" \/><\/p>\n<p>Answer:<br \/>\n258 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 9 x 5 + 9 x 5 + 6 x 9+ 6 x 9\u00a0 + 6 x 5 +6 x 5<br \/>\nsurface area = 45 + 45 + 54 + 54 + 30 +30<br \/>\nsurface area = 258 sq. mm<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-163.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 163\" width=\"187\" height=\"106\" \/><\/p>\n<p>Answer:<br \/>\n286 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 10 x 3.5 + 10 x 3.5 + 10 x 8+ 10 x 8\u00a0 + 8 x 3.5 + 8 x 3.5<br \/>\nsurface area = 35 +35+ 80 + 80 +28 +28<br \/>\nsurface area = 286 sq. ft<\/p>\n<p><strong>Key Idea<\/strong><br \/>\n<strong>Net of a Triangular Prism<\/strong><br \/>\nA triangular prism is a prism with triangular bases.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-164.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 164\" width=\"503\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-164.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-164-300x90.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the surface area of the triangular prism.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-165.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 165\" width=\"172\" height=\"122\" \/><\/p>\n<p>Answer:<br \/>\n67 sq. yd<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 3 x 5 = 15+ (1\/2) x 3 x 4 = 6 + (1\/2) x 3 x 4 = 6 + 4 x 5 = 20 + 5 x 4 = 20<br \/>\nbottom = 3 x 5 , front = (1\/2) x 3 x 4, back = (1\/2) x 3 x 4, side = 4 x 5 , side = 5 x 4<br \/>\nsurface\u00a0 area = 15 +6 +6 +20 + 20<br \/>\narea = 67 sq. yd<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-166.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 166\" width=\"180\" height=\"91\" \/><\/p>\n<p>Answer:<br \/>\n510 sq. m<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 10 x 10 = 100+ (1\/2) x 10 x 16=80 + (1\/2) x 10 x 16 = 80+ 9 x 10 =90 + 10 x 16=160<br \/>\nbottom = 10 x 10 , front = (1\/2) x 10 x 16, back = (1\/2) x 10 x 16, side = 9 x 10 , side = 10 x 16<br \/>\nsurface\u00a0 area = 100 +80 +80+90 +160<br \/>\narea = 510 sq. m<\/p>\n<p>When all the edges of a rectangular prism have the same length s, the rectangular prism is a cube. The net of a cube shows that each of the 6 identical square faces has an area of s<sup>2<\/sup>. So, a formula for the surface area of a cube is<br \/>\nS = 6s<sup>2<\/sup>. Formula for surface area of a cube<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-167.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 167\" width=\"113\" height=\"103\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-168.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 168\" width=\"186\" height=\"144\" \/><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Find the surface area of the cube.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-169.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 169\" width=\"132\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\n96 sq. cm<\/p>\n<p>Explanation:<br \/>\narea of the cube = 6 s2<br \/>\narea = 6 x side x side<br \/>\narea = 6 x 4\u00a0 x 4<br \/>\narea = 96 sq. cm<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-170.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 170\" width=\"131\" height=\"122\" \/><\/p>\n<p>Answer:<br \/>\n1.5 sq. in<\/p>\n<p>Explanation:<br \/>\narea of the cube = 6 s2<br \/>\narea = 6 x side x side<br \/>\narea = 6 x 0.5\u00a0 x 0.5<br \/>\narea = 1.5 sq. in<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\n<strong>FINDING SURFACE AREA<\/strong><br \/>\nFind the surface area of a cube with edge lengths of 9 centimeters.<\/p>\n<p>Answer:<br \/>\n486 sq. cm<\/p>\n<p>Explanation:<br \/>\narea of the cube = 6 s2<br \/>\narea = 6 x side x side given that s = 9 cm<br \/>\narea = 6 x 9\u00a0 x 9<br \/>\narea = 486 sq. cm<\/p>\n<p>Question 8.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-171.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 171\" width=\"155\" height=\"149\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-172.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 172\" width=\"453\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-172.png 453w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-172-300x112.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\nLight shines through a glass prism and forms a rainbow. What is the surface area of the prism?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-173.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 173\" width=\"226\" height=\"160\" \/><\/p>\n<p>Answer:<br \/>\n93 sq. cm<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 6 x 3 = 18+ (1\/2) x 5 x 6=30 + (1\/2) x 5 x 6 = 30+ 3 x 5 =15+ 5 x 6= 30<br \/>\nbottom = 6\u00a0 x 3 , front = (1\/2) x 5 x 6, back = (1\/2) x 5 x 6, side = 3 x 5 , side = 5 x 6<br \/>\nsurface\u00a0 area = 18 +15 +15 +15 +30<br \/>\narea = 93 sq. cm<\/p>\n<p>Question 10.<br \/>\nOne pint of chalkboard paint covers 60 square feet. What is the least number of pints of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 15 feet, a width of 13 feet, and a height of 10 feet? Explain.<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA \ufb02exible metamaterial is developed for use in robotics and prosthetics. A block of metamaterial is in the shape of a cube with a surface area of 600 square centimeters. What is the edge length of the block of metamaterial?<\/p>\n<p>Answer:<br \/>\nThe edge length of the block of metamaterial = 25 square centimeters<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cube = 6 s square<br \/>\narea = 6 x 25 x4<br \/>\narea = 6 x100<br \/>\narea = 600 square centimeters<\/p>\n<h3><a id=\"Surface_Areas_of_Prisms_Homework_&amp;_Practice_7.5\"><\/a>Surface Areas of Prisms Homework &amp; Practice 7.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Draw the front, side, and top views of the solid.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-174.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 174\" width=\"148\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nfront = 1<br \/>\nside = 2<br \/>\ntop = 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32495\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-56-300x54.png\" alt=\"\" width=\"300\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-56-300x54.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-56-768x139.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-56.png 793w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nQuestion 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-174.1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 174.1\" width=\"113\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nfront = 1<br \/>\nside = 1<br \/>\ntop = 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32496\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-57-300x58.png\" alt=\"\" width=\"300\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-57-300x58.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-57-768x148.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-57.png 821w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-174.2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 174.2\" width=\"119\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nfront = 1<br \/>\nside = 2<br \/>\ntop = 2<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32497\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-58-300x61.png\" alt=\"\" width=\"300\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-58-300x61.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-58-768x157.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-58.png 802w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nFind the GCF of the numbers.<\/p>\n<p>Question 4.<br \/>\n18, 72<\/p>\n<p>Answer:<br \/>\n18<\/p>\n<p>Explanation:<br \/>\nThe factors of 18 are = 3 x 3 x 2<br \/>\nThe factors of 72 are = 3 x 3 x 2 x 2 x 2<br \/>\nFrom the above the greatest common factors are = 3 x 3 x 2 =18<\/p>\n<p>Question 5.<br \/>\n44, 110<\/p>\n<p>Answer:<br \/>\n22<\/p>\n<p>Explanation:<br \/>\nThe factors of 44 are = 2 x 2 x 11<br \/>\nThe factors of 110 are = 2\u00a0 x\u00a0 5 x 11<br \/>\nFrom the above the greatest common factors are = 2 x 11 = 22<\/p>\n<p>Question 6.<br \/>\n78, 93<\/p>\n<p>Answer:<br \/>\n3<\/p>\n<p>Explanation:<br \/>\nThe factors of 78 are = 2 x 3 x 13<br \/>\nThe factors of 93 are = 3 x 31<br \/>\nFrom the above the greatest common factors are = 3<\/p>\n<p>Question 7.<br \/>\n60, 96, 156<\/p>\n<p>Answer :<br \/>\n12<\/p>\n<p>Explanation:<br \/>\nThe factors of 60 are = 2 x 2 x 3 x5<br \/>\nThe factors of 96 are = 2 x 2 x 2x 2 x 2 x 3<br \/>\nThe factors of 156 are =2 x 2 x 3 x 13<br \/>\nFrom the above the greatest common factors are = 2 x 2 x 3 = 12<\/p>\n<p><strong>Solve the equation.<\/strong><\/p>\n<p>Question 8.<br \/>\ns &#8211; 5 = 12<\/p>\n<p>Answer:<br \/>\n17<\/p>\n<p>Explanation:<br \/>\ns = 12 + 5<br \/>\ns = 17<\/p>\n<p>Question 9.<br \/>\nx + 9 = 20<\/p>\n<p>Answer:<br \/>\n11<\/p>\n<p>Explanation:<br \/>\nx = 20\u00a0 -9<br \/>\nx = 11<\/p>\n<p>Question 10.<br \/>\n48 = 6r<\/p>\n<p>Answer:<br \/>\nr = 8<\/p>\n<p>Explanation:<br \/>\n48 = 6r<br \/>\nr = (48\/6)<br \/>\nr = 8<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{m}{5}\\) = 13<\/p>\n<p>Answer:<br \/>\n65<\/p>\n<p>Explanation:<br \/>\n(m\/5) = 13<br \/>\nm = 13 x 5<br \/>\nm = 65<\/p>\n<p><strong>Divide.<\/strong><\/p>\n<p>Question 12.<br \/>\n496 \u00f7 16<\/p>\n<p>Answer:<br \/>\n31<\/p>\n<p>Explanation:<br \/>\n(496\/16) = 31<\/p>\n<p>Question 13.<br \/>\n765 \u00f7 45<\/p>\n<p>Answer:<br \/>\n17<\/p>\n<p>Explanation:<br \/>\n(765\/45) = 17<\/p>\n<p>Question 14.<br \/>\n1173 \u00f7 23<\/p>\n<p>Answer:<br \/>\n51<\/p>\n<p>Explanation:<br \/>\n(1173\/23) = 51<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>USING TOOLS<\/strong><br \/>\n<strong>Use a net to \ufb01nd the area of the entire surface of the solid. Explain your reasoning.<\/strong> (See Exploration 2, p. 311.)<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-175.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 175\" width=\"124\" height=\"94\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the rectangle = length x breadth<br \/>\narea = l x b<\/p>\n<p>Explanation:<br \/>\nThe above figure is same as the rectangle<br \/>\nThe surface area of the rectangle = length x breadth<br \/>\narea = l x b<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-176.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 176\" width=\"106\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the triangle =\u00a0 (\/2) x\u00a0 length x breadth<br \/>\narea =(1\/2) x l x b<\/p>\n<p>Explanation:<br \/>\nThe above figure is the same as the triangle<br \/>\nThe surface area of the rectangle =(1\/2) x length x breadth<br \/>\narea =(1\/2) l x b<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-177.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 177\" width=\"145\" height=\"150\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the square =\u00a0 (\/2) x\u00a0 length x breadth<br \/>\narea =(1\/2) x l x b<\/p>\n<p>Explanation:<br \/>\nThe above figure is the same as the triangle<br \/>\nThe surface area of the rectangle =(1\/2) x length x breadth<br \/>\narea =(1\/2) l x b<\/p>\n<p><strong>FINDING SURFACE AREA<\/strong><br \/>\n<strong>Find the surface area of the rectangular prism.<\/strong><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-178.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 178\" width=\"205\" height=\"74\" \/><\/p>\n<p>Answer:<br \/>\n130 ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 5 x 1 + 5 x 1 + 10 x 5 + 10 x 5 + 10 x 1 +10 x 1<br \/>\nsurface area = 5 + 5 + 50 + 50 +10 +10<br \/>\nsurface area = 130<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-179.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 179\" width=\"156\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\n198<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 6 x 9 + 6 x 9 + 9 x 3 + 9 x 3 + 6 x 3 +6 x 3<br \/>\nsurface area = 54 + 54 + 27 + 27 +18 +18<br \/>\nsurface area = 198 sq. cm<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-180.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 180\" width=\"105\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\n76<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 2 x 4+ 2 x 4 + 4 x 5 + 4 x 5 + 2 x 5 +2 x 5<br \/>\nsurface area = 8 + 8 + 20 + 20+10+10<br \/>\nsurface area = 76<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-181.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 181\" width=\"170\" height=\"134\" \/><\/p>\n<p>Answer:<br \/>\n52in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 2 x 4+ 2 x 4 + 3 x 2 + 3 x 2 + 4 x 3 +4 x 3<br \/>\nsurface area = 8 + 8 + 6 + 6 +12 +12<br \/>\nsurface area = 52<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-182.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 182\" width=\"144\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\n116.375 m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 5.5 x 3 + 5.5 x 3 + 3 x 7.25 + 3 x 7.25 + 5.5 x 7.25 + 5.5 x 7.25<br \/>\nsurface area = 16.5+ 16.5 + 21.75 + 21.75 +39.875 +39.875<br \/>\nsurface area = 116.375 m<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-183.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 183\" width=\"216\" height=\"83\" \/><\/p>\n<p>Answer:<br \/>\n48.785 mi<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 6 x2 .33 + 6 x 2.33 + 2.33 x 1.25 + 2.33 x 1.25 + 6 x 1.25 + 6 x 1.25<br \/>\nsurface area = 13.98+ 13.98 + 2.9125 + 2.9125 +7.5 +7.5<br \/>\nsurface area = 48.785 mi<\/p>\n<p><strong>FINDING SURFACE AREA<\/strong><br \/>\n<strong>Find the surface area of the triangular prism.<\/strong><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-184.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 184\" width=\"141\" height=\"135\" \/><\/p>\n<p>Answer:<br \/>\n102 cm<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 3 x 4 = 12 + (1\/2) x 3 x 10 = 15 + (1\/2) x 3 x 10\u00a0 = 15 + 4 x 5 = 20 + 4 x 10 = 40<br \/>\nbottom = 3 x 4 , front = (1\/2) x 3 x 10, back = (1\/2) x 3 x 10, side = 4 x 5 , side = 4 x 10<br \/>\nsurface\u00a0 area = 12 +15 +15+20 +40<br \/>\narea = 102\u00a0 cm<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-185.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 185\" width=\"156\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\n822 m<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 16 x 10 = 160+ (1\/2) x 16 x 17 = 136 + (1\/2) x 16 x 17 = 136+ 15 x 10=150 + 15 x 16 = 240<br \/>\nbottom = 16 x 10 , front = (1\/2) x16 x 17, back = (1\/2) x 16 x 17, side = 15 x 10 , side =15 x 16<br \/>\nsurface\u00a0 = 160 +136+ 136 + 150 + 240<br \/>\narea = 822 m<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-186.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 186\" width=\"127\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\n543 in<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 12 x 9 = 108+ (1\/2) x 12 x 10 = 60 + (1\/2) x 12 x 10 = 60 + 15 x 9 = 135 + 9 x 20 = 180<br \/>\nbottom = 12 x 9 , front = (1\/2) x12 x 10, back = (1\/2) x 12 x 10, side = 115 x 9 , side = 9 x 20<br \/>\nsurface\u00a0 area =108 +60 +60+ 135 +180<br \/>\narea = 543 in<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-187.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 187\" width=\"134\" height=\"123\" \/><\/p>\n<p>Answer:<br \/>\n17.8 ft<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 1 x 3 = 3+ (1\/2) x 1 x 2.2 = 1.1 + (1\/2) x 1 x 2.2 = 1.1 + 2 x 3 = 6+ 3 x 2.2 = 6.6<br \/>\nbottom = 1 x 3 , front = (1\/2) x1 x 2.2, back = (1\/2) x 1 x 2.2, side = 2 x 3 , side = 3 x 2.2<br \/>\nsurface\u00a0 area =3 + 1.1 + 1.1+ 6 + 6.6<br \/>\narea = 17. 8 ft<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-188.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 188\" width=\"162\" height=\"102\" \/><\/p>\n<p>Answer:<br \/>\n62 . 8 mm<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 4 x 4 = 16+ (1\/2) x 4 x 3 = 6 + (1\/2) x\u00a0 4 x 3 = 6 + 5.7 x 4=22.8+ 3 x 4 = 12<br \/>\nbottom = 4 x 4 , front = (1\/2) x 4 x 3, back = (1\/2) x 4 x 3, side = 5.7 x 4 , side = 3 x 4<br \/>\nsurface\u00a0 area = 16 + 6 + 6 +22.8 + 12<br \/>\narea = 62. 8 mm<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-189.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 189\" width=\"156\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\n3228 . 26 m<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 10 x (17\/3) = 56.6+ (1\/2) x 10 x 13 = 65 + (1\/2) x\u00a0 10 x 13 = 65 + 12 x (17\/3) = 68+ (17\/3) x 13 = 73.6<br \/>\nbottom = 10 x (17\/3) , front = (1\/2) x 10 x 13, back = (1\/2) x 10 x 13, side = 12 x (17\/3) , side = (17\/3) x 13<br \/>\nsurface\u00a0 area = 56.6 + 65 + 65 + 68 + 73.6<br \/>\narea = 3228. 26 m<\/p>\n<p>Question 30.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA gift box in the shape of a rectangular prism measures 8 inches by 8 inches by 10 inches. What is the least amount of wrapping paper needed to wrap the gift box? Explain<\/p>\n<p>Answer:<br \/>\n440 inches<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 8 x 8 + 8 x 8 + 10 x 8 + 10 x 8+ 8 x 10 + 8 x 10<br \/>\nsurface area = 64 + 64+ 80 + 80 + 80 + 80<br \/>\nsurface area = 440 in<br \/>\nThe least amount of wrapping paper needed to wrap the gift box = 440 in<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nWhat is the least amount of fabric needed to make the tent?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-190.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 190\" width=\"246\" height=\"160\" \/><\/p>\n<p>Answer:<br \/>\n102 sq. ft<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 6 x 4 = 24+ (1\/2) x 6 x 5 = 15 + (1\/2) x\u00a0 6 x 5 = 15+ 7 x 4 = 28+ 5 x 4 = 20<br \/>\nbottom = 6 x 4 , front = (1\/2) x 6 x 5, back = (1\/2) x 6 x 5, side = 7 x 4 , side = 5 x 4<br \/>\nsurface\u00a0 area = 24 + 15 + 15 + 28 + 20<br \/>\narea = 20 sq. ft<\/p>\n<p><strong>FINDING SURFACE AREA<\/strong><\/p>\n<p><strong>Find the surface area of the cube.<\/strong><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-191.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 191\" width=\"144\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\n216 sq. km<\/p>\n<p>Explanation:<br \/>\narea of the cube = 6 s2<br \/>\narea = 6 x side x side<br \/>\narea = 6 x 6\u00a0 x 6<br \/>\narea = 216 sq. km<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-192.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 192\" width=\"148\" height=\"131\" \/><\/p>\n<p>Answer:<br \/>\n0.66666 sq. ft<\/p>\n<p>Explanation:<br \/>\narea of the cube = 6 s\u00b2<br \/>\narea = 6 x side x side<br \/>\narea = 6 x (1\/2)\u00a0 x (1\/2)<br \/>\narea = 6 x 0.11111<br \/>\narea = 0.6666 sq. ft<\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-193.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 193\" width=\"155\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\n181.5 sq. yd<\/p>\n<p>Explanation:<br \/>\narea of the cube = 6 s\u00b2<br \/>\narea = 6 x side x side<br \/>\narea = 6 x 5.5 x 5.5<br \/>\narea = 6 x 30.25<br \/>\narea = 181 .5 sq. yd<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA piece of dry ice is in the shape of a cube with edge lengths of 7 centimeters. Find the surface area of the dry ice.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-194.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 194\" width=\"209\" height=\"294\" \/><\/p>\n<p>Answer:<br \/>\n294 centimeters<br \/>\nExplanation:<br \/>\narea of the cube = 6 s2<br \/>\narea = 6 x side x side<br \/>\narea = 6 x 7 x 7<br \/>\narea = 6 x 49<br \/>\narea = 294 sq. cm<\/p>\n<p>Question 36.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the surface area of the prism. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-195.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 195\" width=\"317\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-195.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-195-300x148.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/p>\n<p>Answer:<br \/>\nNo, my friend is not correct because my friend did the surface area of the cube<\/p>\n<p>Explanation:<br \/>\nMy friend did the surface area of the cube<br \/>\ncube = 6s\u00b2<\/p>\n<p>Question 37.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA public library has the aquarium shown. The front piece of glass has an area of 24 square feet. How many square feet of glass were used to build the aquarium?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-196.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 196\" width=\"272\" height=\"198\" \/><\/p>\n<p>Answer:<br \/>\nThe square feet of glass were used to build the aquarium = 12 ft<\/p>\n<p>Explanation:<br \/>\nThe square feet of glass were\u00a0 used to build the aquarium = l x b<br \/>\nsquare = 6 x 2.5<br \/>\nsquare = 12<\/p>\n<p>Question 38.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA cereal box has the dimensions shown.<br \/>\na. Find the surface area of the cereal box.<br \/>\nb. The manufacturer decides to decrease the size of the box by reducing each of the dimensions by 1 inch. Find the decrease in surface area.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-197.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 197\" width=\"190\" height=\"206\" \/><\/p>\n<p>Answer:<br \/>\na : 216 in<br \/>\nb : 144 in<\/p>\n<p>Explanation:<br \/>\nSurface area\u00a0 of a = 6 x s x s<br \/>\narea = 6 x 36<br \/>\narea = 216<br \/>\nsurface area of b = 6 x s x s<br \/>\narea = 6 x 24<br \/>\narea = 144 because they said that cereal box is decreased by 1 inch<\/p>\n<p>Question 39.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe material used to make a storage box costs $1.25 per square foot. The boxes have the same volume. Which box might a company prefer to make? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-198.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 198\" width=\"263\" height=\"113\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>LOGIC<\/strong><br \/>\nWhich of the following are nets of a cube? Select all that apply.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-199.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 199\" width=\"577\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-199.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-199-300x66.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 41.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA quart of stain covers 100 square feet. How many quarts should you buy to stain the wheelchair ramp? (Assume you do not have to stain the bottom of the ramp.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-200.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 200\" width=\"380\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-200.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-200-300x119.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p>Answer:<\/p>\n<p>Question 42.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA cube is removed from a rectangular prism. Find the surface area of the \ufb01gure after removing the cube.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-201.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 201\" width=\"211\" height=\"165\" \/><\/p>\n<p>Answer:<br \/>\n341 sq. ft<\/p>\n<p>Explanation:<br \/>\nSurface area of the rectangular prism = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area =\u00a0 9 x 8= 72 + (1\/2) x 9 x 5=94.5 + (1\/2) x 9 x 5 = 94.5 + 5 x 8 = 40+ 8 x 5 =40<br \/>\nbottom = 9 x 8 , front = (1\/2) x 9 x 5, back = (1\/2) x 9 x 5, side = 5 x 8 , side = 8 x 5<br \/>\nsurface\u00a0 area = 72 + 94.5 + 94.5 +40 +40<br \/>\narea = 341 sq. ft<\/p>\n<h3><a id=\"Lesson_7.6_Surface_Areas_of_Pyramids\"><\/a>Lesson 7.6 Surface Areas of Pyramids<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Using a Net to Construct a Solid<\/strong><br \/>\n<strong>Work with a partner. Copy the net shown below onto grid paper.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-202.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 202\" width=\"603\" height=\"360\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-202.png 603w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-202-300x179.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><br \/>\na. Cut out and fold the net to form a solid. What type of solid does the net form?<br \/>\nb. What is the surface area of the solid?<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Finding Surface Areas of Solids<\/strong><br \/>\n<strong>Work with a partner. Find the surface area of each solid. Explain your reasoning.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-203.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 203\" width=\"496\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-203.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-203-300x87.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-204.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 204\" width=\"148\" height=\"186\" \/><\/p>\n<p><strong>7.6 Lesson<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-205.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 205\" width=\"533\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-205.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-205-300x132.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><br \/>\nIn this book, the base of every pyramid is either a square or an equilateral triangle. So, the lateral faces are identical triangles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-206.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 206\" width=\"185\" height=\"197\" \/><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Find the surface area of the square pyramid.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-207.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 207\" width=\"122\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\n16 sq. ft<\/p>\n<p>Explanation:<br \/>\nsurface area of the square pyramid = bottom + side + side + side + side<br \/>\narea = 4 + 3 + 3 + 3<br \/>\nbottom = 2 x 2= 4, side = (1\/2) x 2 x 3 = 3,<br \/>\narea = 16 sq. ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-208.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 208\" width=\"152\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\n62.5 sq. cm<br \/>\nExplanation:<br \/>\nsurface area of the square pyramid = bottom + side + side + side + side<br \/>\narea = 25 + 12.5 + 12.5 + 12.5<br \/>\nbottom = 5 x 5 = 25, side = (1\/2) x 5 x 5 = 12.5,<br \/>\narea = 62.5 sq. cm<\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Find the surface area of the triangular pyramid.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-209.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 209\" width=\"131\" height=\"137\" \/><\/p>\n<p>Answer:<br \/>\narea = 26 sq. cm<\/p>\n<p>Explanation:<br \/>\nsurface area of the triangular pyramid = bottom + side + side + side<br \/>\narea = 17 + 3 + 3 + 3<br \/>\nbottom = (1\/2 ) x 3 x 4 = 17 , side =(1\/2) x 3 x 2 = 3<br \/>\narea = 26 sq. cm<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-210.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 210\" width=\"156\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\narea = 26 sq. cm<\/p>\n<p>Explanation:<br \/>\nsurface area of the triangular pyramid = bottom + side + side + side<br \/>\narea = 17 + 3 + 3 + 3<br \/>\nbottom = (1\/2 ) x 3 x 4 = 17 , side =(1\/2) x 3 x 2 = 3<br \/>\narea = 26 sq. cm<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\n<strong>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/strong><\/p>\n<p>Question 5.<br \/>\n<strong>PRECISION<\/strong><br \/>\nExplain how to \ufb01nd the surface area of a pyramid.<\/p>\n<p>Answer:<br \/>\nSurface area of the pyramid = area +(1\/2) x p x s<\/p>\n<p>Explanation:,<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s where p = perimeter of the base, s = slant height<\/p>\n<p><strong>FINDING SURFACE AREA<\/strong><br \/>\n<strong>Find the surface area of the pyramid.<\/strong><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-211.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 211\" width=\"203\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nArea = 21 sq. yd<\/p>\n<p>Explanation:,<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s where p = perimeter of the base, s = slant height<br \/>\narea = 7 +(1\/2) x 4 x 7<br \/>\narea = 7 + 14<br \/>\narea = 21 sq. yd<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-212.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 212\" width=\"157\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-212.png 157w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-212-150x150.png 150w\" sizes=\"(max-width: 157px) 100vw, 157px\" \/><\/p>\n<p>Answer:<br \/>\nArea = 31.15 sq. m<\/p>\n<p>Explanation:,<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s where p = perimeter of the base, s = slant height<br \/>\narea = 8 +(1\/2) x 7 x\u00a0 6.9<br \/>\narea = 7 + (48.3\/2)<br \/>\narea = 7 + 24.15<br \/>\narea = 31.15 sq. m<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 8.<br \/>\nA salt lamp is shaped like a triangular pyramid. Find the surface area of each triangular face.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-213.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 213\" width=\"184\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the triangular pyramid = 115.5 sq. in<\/p>\n<p>Explanation:<\/p>\n<p>The surface area of the triangular pyramid = area of the faces + area of the base<br \/>\narea of the face1 = 3 in<br \/>\narea of the face2 = 3 in<br \/>\narea of the face3\u00a0 = 3 in<br \/>\narea of the face4 = 3in<br \/>\narea of the base = 3.5<br \/>\nsurface area = 12 + 3.5 = 15.5 sq. in<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nOriginally, each triangular face of the Great Pyramid of Giza had a height of 612 feet and a base of 756 feet. Today, the height of each triangular face of the square pyramid is 592 feet. Find the change in the total surface area of the four triangular faces of the Great Pyramid of Giza.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-214.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 214\" width=\"194\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the\u00a0 four triangular faces = 612 sq. ft<\/p>\n<p>Explanation:<\/p>\n<p>The surface area of the triangular pyramid = area of the faces + area of the base<br \/>\narea of the face1 = 612 sq. ft<br \/>\narea of the face2 = 612 sq. ftft<br \/>\narea of the face3\u00a0 =612 sq. ft<br \/>\narea of the face4 = 612 sq. ft<br \/>\narea of the base = 756 sq. ft<br \/>\nsurface area = 3204 sq. ft<\/p>\n<h3><a id=\"Surface_Areas_of_Pyramids_Homework_&amp;_Practice_7.6\"><\/a>Surface Areas of Pyramids Homework &amp; Practice 7.6<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the surface area of the prism.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-215.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 215\" width=\"166\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\n82 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 7 x 2 + 7 x 2 + 7 x 3+ 7 x 3 + 3 x 2 + 3 x 2<br \/>\nsurface area = 14 +14+ 21 + 21 +6+6<br \/>\nsurface area = 82 sq. ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-216.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 216\" width=\"160\" height=\"142\" \/><\/p>\n<p>Answer:<br \/>\n82 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area =\u00a0 + 7 x 2 + 7 x 3+ 7 x 3 + 3 x 2 + 3 x 2<br \/>\nsurface area = 14 +14+ 21 + 21 +6+6<br \/>\nsurface area = 82 sq. ft<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-217.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 217\" width=\"149\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\n384 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area =8 x 8\u00a0 + 8 x 8 + 8 x 8+ 8 x 8 + 8 x 8 + 8 x 8<br \/>\nsurface area = 64 +64 + 64 + 64+ 64+64<br \/>\nsurface area = 384 sq. in<\/p>\n<p><strong>Match the expression with an equivalent expression.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-218.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 218\" width=\"104\" height=\"64\" \/><\/p>\n<p>Answer:<br \/>\n12n + 6<br \/>\nA. 12n + 12<\/p>\n<p>Explanation:<br \/>\n3 x (4n + 2 )<br \/>\n12n + 6<br \/>\nA. 2 x (6n + 6)<br \/>\n12n + 12<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-219.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 219\" width=\"102\" height=\"58\" \/><\/p>\n<p>Answer:<br \/>\n12n + 18<br \/>\nB. 6(2n + 3)<\/p>\n<p>Explanation:<br \/>\n6 x (2n + 3 )<br \/>\n12n + 18<br \/>\nA. 6 x (2n + 3)<br \/>\n12n + 18<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-220.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 220\" width=\"103\" height=\"62\" \/><\/p>\n<p>Answer:<br \/>\n12n + 16<br \/>\nC. 12n + 6<\/p>\n<p>Explanation:<br \/>\n4 x (3n + 4 )<br \/>\n12n + 16<br \/>\nC.\u00a0 2 x (6n + 3)<br \/>\n12n + 6<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-221.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 221\" width=\"109\" height=\"63\" \/><\/p>\n<p>Answer:<br \/>\n12n + 12<br \/>\nD. 2 x (6n +8)<\/p>\n<p>Explanation:<br \/>\n4 x (3n + 3)<br \/>\n12n + 12<br \/>\nC.\u00a0 2 x (6n + 8)<br \/>\n12n + 16<\/p>\n<p><strong>Write the fraction or mixed number as a percent.<\/strong><\/p>\n<p>Question 8.<br \/>\n\\(\\frac{17}{25}\\)<\/p>\n<p>Answer:<br \/>\n68%<\/p>\n<p>Explanation:<br \/>\n(17\/25) = (17\/25 x 100)<br \/>\n(17 x 4)\/(25 x 4)<br \/>\n(68\/100)<br \/>\n(34\/50)<br \/>\n68%<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{19}{20}\\)<\/p>\n<p>Answer:<br \/>\n95%<\/p>\n<p>Explanation:<br \/>\n(19\/20) = (19\/20 x 100)<br \/>\n(19 x 5)\/(20 x 5)<br \/>\n(95\/100)<br \/>\n95%<br \/>\nQuestion 10.<br \/>\n6\\(\\frac{7}{8}\\)<\/p>\n<p>Answer:<br \/>\n6.875%<\/p>\n<p>Explanation:<br \/>\n(7\/8) = (7\/8 x 100)<br \/>\n6 x (7\/8) = 6 x (7\/8 x 100)<br \/>\n(55\/8)<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{3}{400}\\)<\/p>\n<p>Answer:<br \/>\n0.75%<\/p>\n<p>Explanation:<br \/>\n(3\/400) = (3\/400 x 100)<br \/>\n(3\/4) = 0.75%<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>USING TOOLS<\/strong><br \/>\n<strong>Use a net to \ufb01nd the surface area of the solid. Explain your reasoning.<\/strong> (See Exploration 2, p. 319.)<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-222.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 222\" width=\"157\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the triangular pyramid = a+(1\/2) x p x s<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s where p = perimeter of the base, s = slant height<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-223.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 223\" width=\"163\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the triangular pyramid = a+(1\/2) x p x s<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s where p = perimeter of the base, s = slant height<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-224.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 224\" width=\"213\" height=\"91\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the triangular pyramid = a+(1\/2) x p x s<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s where p = perimeter of the base, s = slant height<\/p>\n<p><strong>FINDING SURFACE AREA<\/strong><br \/>\n<strong>Find the surface area of the pyramid.<\/strong><\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-225.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 225\" width=\"167\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the\u00a0 pyramid = 27 in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = area of the faces + area of the base<br \/>\narea of the face1 = 5 sq. in<br \/>\narea of the face2 = 5 sq. in<br \/>\narea of the face3\u00a0 = 5 sq. in<br \/>\narea of the face4 = 5 sq. in<br \/>\narea of the base = 7 sq. in<br \/>\nsurface area = 27 sq. in<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-226.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 226\" width=\"133\" height=\"153\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the\u00a0 pyramid = 51 .6 sq. yd<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = area of the faces + area of the base<br \/>\narea of the face1 = 11.4 sq. yd<br \/>\narea of the face2 = 11.4 sq. yd<br \/>\narea of the face3\u00a0 = 11.4 sq. yd<br \/>\narea of the face4 = 11.4 sq. yd<br \/>\narea of the base = 6 sq. yd<br \/>\nsurface area = 51.6 sq. yd<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-227.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume 227\" width=\"141\" height=\"152\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the\u00a0 pyramid = 80 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = area of the faces + area of the base<br \/>\narea of the face1 = 17 sq. cm<br \/>\narea of the face2 = 17 sq. cm<br \/>\narea of the face3\u00a0 = 17 sq. cm<br \/>\narea of the face4 = 17 sq. cm<br \/>\narea of the base = 12 sq. cm<br \/>\nsurface area = 80 sq. cm<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-228.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 228\" width=\"154\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the\u00a0 pyramid = 50.8 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = area of the faces + area of the base<br \/>\narea of the face1 = 10.4 sq. ft<br \/>\narea of the face2 = 10.4 sq. ft<br \/>\narea of the face3\u00a0 = 9 sq. ft<br \/>\narea of the face4 = 9 sq. ft<br \/>\narea of the base = 12 sq. ft<br \/>\nsurface area = 50.8 sq. ft<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-229.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 229\" width=\"131\" height=\"157\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the\u00a0 pyramid = 49.8 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = area of the faces + area of the base<br \/>\narea of the face1 = 6.9 sq. in<br \/>\narea of the face2 = 6.9 sq. in<br \/>\narea of the face3\u00a0 = 14 sq. in<br \/>\narea of the face4 = 14 sq. in<br \/>\narea of the base = 8 sq. in<br \/>\nsurface area = 49.8 sq. in<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-230.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 230\" width=\"114\" height=\"152\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the\u00a0 pyramid = 27 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = area of the faces + area of the base<br \/>\narea of the face1 = 8 sq. m<br \/>\narea of the face2 = 8 sq. m<br \/>\narea of the face3\u00a0 = 3.5 sq. m<br \/>\narea of the face4 = 3.5 sq. m<br \/>\narea of the base = 4 sq. m<br \/>\nsurface area = 27 sq. m<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA paperweight is shaped like a triangular pyramid. Find the surface area of the paperweight.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-231.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 231\" width=\"127\" height=\"140\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the\u00a0 pyramid = 9.8 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = area of the faces + area of the base<br \/>\narea of the face1 = 2.2 sq. in<br \/>\narea of the face2 = 2.2 sq. in<br \/>\narea of the face3\u00a0 = 1.7 sq. in<br \/>\narea of the face4 = 1.7 sq. in<br \/>\narea of the base = 2 sq. in<br \/>\nsurface area = 9.8 sq. in<\/p>\n<p>Question 22.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe entrance to the Louvre Museum in Paris, France, is a square pyramid. The side length of the base is 116 feet, and the height of one of the triangular faces is 91.7 feet. Find the surface area of the four triangular faces of the entrance to the LouvreMuseum.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-232.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 232\" width=\"265\" height=\"165\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the\u00a0 pyramid = 48.2 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = area of the faces + area of the base<br \/>\narea of the face1 = 91.7 sq. ft<br \/>\narea of the face2 = 91.7 sq. ft<br \/>\narea of the face3\u00a0 = 91.7 sq. ft<br \/>\narea of the face4 = 91.7 sq. ft<br \/>\narea of the base = 116 sq. ft<br \/>\nsurface area = 482.8 sq. ft<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA silicon wafer is textured to minimize light re\ufb02ection. This results in a surface made up of square pyramids. Each triangular face of one of the pyramids has a base of 5 micrometers and a height of 5.6 micrometers.Find the surface area of the pyramid, including the base.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-233.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 233\" width=\"226\" height=\"173\" \/><\/p>\n<p>Answer:<br \/>\nArea = 42 sq. micrometers<\/p>\n<p>Explanation:,<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s where p = perimeter of the base, s = slant height<br \/>\narea = 28 +(1\/2) x 5 x 5.6<br \/>\narea = 28+ (28\/2)<br \/>\narea = 28+ 14<br \/>\narea = 42 sq. micrometers<\/p>\n<p>Question 24.<br \/>\n<strong>REASONING<\/strong><br \/>\nA hanging light cover made of glass is shaped like a square pyramid. The cover does not have a bottom. One square foot of the glass weighs 2.45 pounds. The chain can support 35 pounds. Will the chain support the light cover? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-234.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 234\" width=\"211\" height=\"206\" \/><\/p>\n<p>Answer:<br \/>\nYes the chain support the light cover<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s where p = perimeter of the base, s = slant height<br \/>\narea = 4+(1\/2) x 2\u00a0 x 2<br \/>\narea = 4+ 4<br \/>\narea = 8<br \/>\narea = 8 sq. ft<\/p>\n<p>Question 25.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe surface area of the square pyramid shown is 84 square inches. What is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-235.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 235\" width=\"181\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nThe value of x = 14 in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square pyramid = length x breadth<br \/>\narea = l x b<br \/>\n84 =6x<br \/>\nx =(84\/6)<br \/>\nx =14 in<\/p>\n<p>Question 26.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nIn the diagram of the base of the hexagonal pyramid, all the triangles are the same. Find the surface area of the hexagonal pyramid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-236.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 236\" width=\"339\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-236.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-236-300x144.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the hexagonal pyramid = 478.32 cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the hexagonal pyramid = 3ab +3bs<br \/>\narea = 3 x 8 x 6.93 +3 x 8 x 13 where a = 8,b =8, s = 13<br \/>\narea = 166.32+312<br \/>\narea = 478.32 sq. cm<\/p>\n<p>Question 27.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nCan you form a square pyramid using a square with side lengths of 14 inches and four of the triangles shown? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-237.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 237\" width=\"218\" height=\"131\" \/><\/p>\n<p>Answer:<br \/>\nyes<br \/>\nExplanation:<br \/>\ngiven that square has side lengths of 14 inches and four of the triangles.<br \/>\nso we can form the square pyramid<\/p>\n<h3><a id=\"Lesson_7.7_Volumes_of_Rectangular_Prisms\"><\/a>Lesson 7.7 Volumes of Rectangular Prisms<\/h3>\n<p>Recall that the volume of a three-dimensional \ufb01gureis a measure of the amount of space that it occupies. Volume is measured in cubic units.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Using a Unit Cube<\/strong><br \/>\n<strong>Work with a partner. A unit cube is a cube with an edge length of 1 unit. The parallel edges of the unit cube have been divided into 2, 3, and 4 equal parts to create smaller rectangular prisms that are identical.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-238.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 238\" width=\"245\" height=\"164\" \/><br \/>\na. The volumes of the identical prisms are equal. What else can you determine about the volumes of the prisms? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-239.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 239\" width=\"178\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 1 unit<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh<br \/>\nwhere b = area of the base<br \/>\nvolume = 1 x 1<br \/>\nvolume = 1<br \/>\nb. Use the identical prisms in part(a) to \ufb01nd the volume of the prism below. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-240.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 240\" width=\"216\" height=\"169\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 4.3125 cu. unit<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh<br \/>\nwhere b = area of the base<br \/>\nvolume = (3\/4) x (2\/3)<br \/>\nvolume = 0.75 x 5.75<br \/>\nvolume = 4.3125 cu. units<\/p>\n<p>c. How can you use a unit cube to \ufb01nd the volume of the prism below? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-241.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 241\" width=\"144\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 0.375 cu. m<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh<br \/>\nwhere b = area of the base<br \/>\nvolume = (1\/2) x (3\/4)<br \/>\nvolume = 0.5x 0.75<br \/>\nvolume = 0.375 cu. m<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-242.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 242\" width=\"162\" height=\"171\" \/><br \/>\nd. Do the formulas V = Bh and V = \u2113wh work for rectangular prisms with fractional edge lengths? Give examples to support your answer.<\/p>\n<p><strong>7.7 Lesson<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nVolume of a Rectangular Prism<br \/>\n<strong>Words<\/strong><br \/>\nThe volume V of a rectangular prism is the product of the area of the base and the height of the prism.<br \/>\n<strong>Algebra<\/strong><br \/>\nV = Bh or V = lwh<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-243.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 243\" width=\"211\" height=\"119\" \/><br \/>\nWhen a rectangular prism is a cube with an edge length of s, you can also use the formula V = s<sup>3<\/sup> to \ufb01nd the volume V of the cube.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-243.1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 243.1\" width=\"204\" height=\"82\" \/><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Find the volume of the prism.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-244.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 244\" width=\"210\" height=\"139\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 0.6665 cu. ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (1.333) x (0.5)<br \/>\nvolume = 1.33 x 0.5<br \/>\nvolume = 0.6665 cu. ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-245.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 245\" width=\"162\" height=\"155\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 0.6665 cu. ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (1.333) x (0.5)<br \/>\nvolume = 1.33 x 0.5<br \/>\nvolume = 0.6665 cu. ft<\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Find the missing dimension of the prism.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-246.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 246\" width=\"183\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nThe missing dimension of the prism = 6 in<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = b x l x h<br \/>\nvolume = 6x 6 x\u00a0 2<br \/>\nvolume = 72 in<br \/>\nso length = 6 in<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-247.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 247\" width=\"203\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nThe width of the prism = 12.5 cm<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = 5 x(1\/2) x 12.5 x20<br \/>\nvolume = (11\/2)x 12.5 x\u00a0 20<br \/>\nvolume = 1375 cm<br \/>\nso width = 12.5 cm<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nExplain how volume and surface area are different.<\/p>\n<p>Answer:<br \/>\nVolume grows exponentially and the surface area grows\u00a0 with the volume<br \/>\nthe surface area grows with the rate of volume<\/p>\n<p>Question 6.<br \/>\n<strong>FINDING A MISSING DIMENSION<\/strong><br \/>\nThe base of a rectangular prism has an area of 24 square millimeters. The volume of the prism is 144 cubic millimeters. Make a sketch of the prism. Then \ufb01nd the height of the prism.<\/p>\n<p>Answer:<br \/>\nThe height of the prism = 6 millimeters<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular prism = Bh<br \/>\nwhere b = base area and h= height<br \/>\nso volume = 144 cubic millimeters given<br \/>\nB = 24<br \/>\nvolume = Bh<br \/>\n144 = 24h<br \/>\nh = (144\/24)<br \/>\nh = 6 mm<\/p>\n<p><strong>FINDING VOLUME<\/strong><br \/>\n<strong>Find the volume of the prism.<\/strong><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-278.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 278\" width=\"181\" height=\"148\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 0.2343 cu. m<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (3\/4) x(1\/2) x (5\/8)<br \/>\nvolume = 0.75 x 0.5x 0.625<br \/>\nvolume = 0.2343 cu. m<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-279.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 279\" width=\"154\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 0.343 cu. in<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (7\/10) x(7\/10) x (7\/10)<br \/>\nvolume = 0.7 x 0.7 x 0.7<br \/>\nvolume = 0.343 cu. in<\/p>\n<p>When \ufb01nding volumes, you may need to convert cubic units. The diagrams at the left show that there are 27 cubic feet per cubic yard.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-280.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 280\" width=\"206\" height=\"108\" \/><br \/>\n1 yd<sup>3<\/sup> = (1 yd)(1 yd)(1 yd) = (3 ft)(3 ft)(3 ft) = 27 ft<sup>3<\/sup><br \/>\nYou can use a similar procedure to convert other cubic units.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe shark cage is in the shape of a rectangular prism and has a volume of 315 cubic feet. Find a set of reasonable dimensions for the base of the cage. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-281.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 281\" width=\"188\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\nThe base\u00a0 of the prism = 4.906 ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\n314 = (8) x(8 ) x h<br \/>\n314 = 64h<br \/>\nh = (314\/64)<br \/>\nh = 4.906 ft<\/p>\n<p>Question 10.<br \/>\nThe hot tub is in the shape of a rectangular prism. How many pounds of water can the hot tub hold? One cubic foot of water weighs about 62.4 pounds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-282.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 282\" width=\"215\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\nThe hot tub can hold = 312 pounds<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nhot tub = (2) x(2) x 1.25<br \/>\nhot tub = 4 x 1.25<br \/>\nhottub = 5<br \/>\nhot tub = 5<br \/>\n5 x 62.4 = 312 pounds<\/p>\n<h3><a id=\"Volumes_of_Rectangular_Prisms_Homework_&amp;_Practice_7.7\"><\/a>Volumes of Rectangular Prisms Homework &amp; Practice 7.7<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the surface area of the pyramid.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-283.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 283\" width=\"115\" height=\"161\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the pyramid = 220.5 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s<br \/>\nwhere area = l x w<br \/>\nsurface area =21 x (1\/2) x 7 x3<br \/>\nsurface area = 21x 10.5<br \/>\nsurface area = 220.5 sq. ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-284.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 284\" width=\"143\" height=\"161\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the pyramid = 364.5 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s<br \/>\nwhere area = l x w<br \/>\nsurface area =27 x (1\/2) x 4.5 x6<br \/>\nsurface area = 27 x (27\/2)=13.5<br \/>\nsurface area = 364.5 sq. m<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-285.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 285\" width=\"173\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the pyramid = 20,760 sq. yd<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = area + (1\/2) x p x s<br \/>\nwhere area = l x w<br \/>\nsurface area =346 x (1\/2) x 12 x 20<br \/>\nsurface area = 346 x (120\/2)=60<br \/>\nsurface area = 20,760 sq. yd<\/p>\n<p>Write the phrase as an expression. Then evaluate the expression when x = 2 and y = 12.<\/p>\n<p>Question 4.<br \/>\n8 more than a number x<\/p>\n<p>Answer:<br \/>\nYes<br \/>\nExplanation:<br \/>\n8 is more than 2<br \/>\nwhere x = 2 given<\/p>\n<p>Question 5.<br \/>\nthe difference of a number y and 9<\/p>\n<p>Answer:<br \/>\nThe difference of a number y and 9 = 3<\/p>\n<p>Explanation:<br \/>\ndifference = 12 &#8211; 9<br \/>\ndiff = 3<br \/>\nwhere y = 12 given<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>STRUCTURE<\/strong><br \/>\n<strong>The unit cube is divided into identical rectangular prisms. What is the volume of one of the identical prisms?<\/strong> (See Exploration 1, p. 325.)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-286.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 286\" width=\"150\" height=\"137\" \/><\/p>\n<p>Answer:<br \/>\n(2\/2),(2\/4),(4\/2)<\/p>\n<p>Explanation:<br \/>\nIn the above figure the base = (2\/2) units<br \/>\nbase = (2\/2) units<br \/>\nheight = (4\/2) units<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-287.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 287\" width=\"157\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\n(3\/3),(3\/2),(2\/3)<\/p>\n<p>Explanation:<br \/>\nIn the above figure the base = (3\/3) units<br \/>\nbase = (3\/2) units<br \/>\nheight = (2\/3) units<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-288.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 288\" width=\"153\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\n(5\/5),(5\/3),(3\/5)<\/p>\n<p>Explanation:<br \/>\nIn the above figure the base = (5\/5) units<br \/>\nbase = (5\/3) units<br \/>\nheight = (3\/5) units<\/p>\n<p><strong>FINDING VOLUME<\/strong><br \/>\n<strong>Find the volume of the prism.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-289.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 289\" width=\"153\" height=\"146\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 0.297 Cu. in<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (0.66) x(0.6) x (0.75)<br \/>\nvolume = 0.297 Cu. in<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-290.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 290\" width=\"194\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 1.3125 Cu. cm<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (7\/4) x(3\/2) x (1\/2)<br \/>\nvolume = 1.75 x 1.5 x 0.5<br \/>\nvolume = 1.3125 Cu. cm<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-291.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 291\" width=\"157\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 0.064 Cu. ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (2\/5) x(2\/5) x (2\/5)<br \/>\nvolume = 0.4 x 0.4 x 0.4<br \/>\nvolume = 0.064 Cu. ft<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-292.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 292\" width=\"124\" height=\"170\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism =0.75 Cu. m<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (5\/8) x(3\/4) x (2)<br \/>\nvolume = 0.625 x 0.6 x 2<br \/>\nvolume = 0.75 Cu. m<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-293.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 293\" width=\"131\" height=\"188\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism =3.111255 Cu. cm<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (5\/3) x(5\/6) x (9\/4)<br \/>\nvolume = 1.66 x 0.833 x 2.25<br \/>\nvolume = 3.111255 Cu. cm<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-294.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 294\" width=\"181\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 12.425 Cu. m<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (14\/5) x(10\/7) x (25\/8)<br \/>\nvolume = 2.8 x 1.42 x 3.125<br \/>\nvolume = 12.425 Cu. m<\/p>\n<p><strong>FINDING A MISSING DIMENSION<\/strong><br \/>\n<strong>Find the missing dimension of the prism.<\/strong><\/p>\n<p>Question 15.<br \/>\nVolume = 1620 cm<sup>3<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-295.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 295\" width=\"126\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\nThe missing dimension of the prism = 20 cm<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\n1620 = (9) x(9) x h<br \/>\n1620 = 81 h<br \/>\nh = (1620\/8)<br \/>\nh = 8<br \/>\nQuestion 16.<br \/>\nVolume = 220.5 cm<sup>3<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-296.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 296\" width=\"151\" height=\"123\" \/><\/p>\n<p>Answer:<br \/>\nThe missing dimension of the prism = 4.5 cm<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\n220.5 = (7) x(7) x w<br \/>\n220.5 = 49 w<br \/>\nw = (220.5\/49)<br \/>\nw = 4.5 cm<\/p>\n<p>Question 17.<br \/>\nVolume = 532 in<sup>3<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-297.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 297\" width=\"225\" height=\"103\" \/><\/p>\n<p>Answer:<br \/>\nThe missing dimension of the prism = 16 in<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\n532 = (7\/4) x(19) x w<br \/>\n532 = 33.25<br \/>\nh = (532\/33.25)<br \/>\nh = 16 in<\/p>\n<p>Question 18.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nAn FBI agent orders a block of ballistics gel. The gel weighs 54 pounds per cubic foot. What is the weight of the block of gel?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-298.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 298\" width=\"267\" height=\"155\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 720 in<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (6) x(20) x 6<br \/>\nvolume = 720 in<br \/>\nQuestion 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\na. Estimate the amount of casserole left in the dish.<br \/>\nb. Will the casserole \ufb01t in the storage container? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-299.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 299\" width=\"425\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-299.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-299-300x143.png 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>Answer:<br \/>\na : The amount of casserole left in the dish = 396 in<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (2.75) x(12) x 12<br \/>\nvolume = 396<\/p>\n<p>b : The casserole will not fit in the container<\/p>\n<p>Explanation:<br \/>\nThe length of the container is less than the casserole<\/p>\n<p>Question 20.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nHow many \\(\\frac{3}{4}\\)-centimeter cubes do you need to create a cube with an edge length of 12 centimeters?<\/p>\n<p>Answer:<br \/>\n16 cubes<\/p>\n<p>Explanation:<br \/>\n16 cubes are used to create a cube with an edge length of 12 centimeters<br \/>\nin the above-given question (3\/4) = 0.75<br \/>\n0.75 x 16 = 12<\/p>\n<p>Question 21.<br \/>\n<strong>REASONING<\/strong><br \/>\nHow many one-millimeter cubes do you need to \ufb01ll a cube that has an edge length of 1 centimeter? How can this result help you convert a volume from cubic millimeters to cubic centimeters? from cubic centimeters to cubic millimeters?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-300.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 300\" width=\"207\" height=\"134\" \/><\/p>\n<p>Answer:<br \/>\n10 mm cubes are needed to fill a cube that has an edge length of 1 cm<\/p>\n<p>Explanation:<br \/>\n1 mm =0.1 cm<br \/>\n0.1 x 10 = 1 cm<br \/>\n1 cubic mm = 0.001 cubic cm<br \/>\n1 cubic cm = 1000 cubic mm<\/p>\n<p>Question 22.<br \/>\n<strong>LOGIC<\/strong><br \/>\nThe container is partially \ufb01lled with unit cubes. How many unit cubes \ufb01t in the container? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26172\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-301.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 301\" width=\"145\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\n6 cubes fit in the container<\/p>\n<p>Explanation:<br \/>\nIn the above diagram,6 units are filled with color<br \/>\nso 6 unit cubes fit in the container.<\/p>\n<p>Question 23.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe area of the shaded face is 96 square centimeters. What is the volume of the rectangular prism?<\/p>\n<p>Answer:<br \/>\nThe volume of the rectangular prism = 4 x 3 x 8<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular prism = length x width x height<br \/>\nvolume = 4 x 3 x 8<\/p>\n<p>Question 24.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIs the combined volume of a 4-foot cube and a 6-foot cube equal to the volume of a 10-foot cube? Use a diagram to justify your answer.<\/p>\n<p>Question 25.<br \/>\n<strong>PROJECT<\/strong><br \/>\nYou have 1400 square feet of boards to use for a new tree house.<br \/>\na. Design a tree house that has a volume of at least 250 cubic feet. Include sketches of your tree house.<br \/>\nb. Are your dimensions reasonable? Explain your reasoning.<\/p>\n<h3><a id=\"Area,_Surface_Area,_and_Volume_Connecting_Concepts\"><\/a>Area, Surface Area, and Volume Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nA sports complex has two swimming pools that are shaped like rectangular prisms. The amount of water in the smaller pool is what percent of the amount of water in the larger pool?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-302.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 302\" width=\"504\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-302.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-302-300x90.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><br \/>\n<strong>Understand the problem.<\/strong><br \/>\nYou know the shape and the dimensions of the two swimming pools. You are asked to \ufb01nd the amount of water in the smaller pool as a percent of the amount of water in the larger pool.<br \/>\n<strong>Make a plan.<\/strong><br \/>\nFirst, \ufb01nd the volume of each pool. Then represent the amount of water in the smaller pool as a fraction of the amount of water in the larger pool. Find an equivalent fraction whose denominator is 100 to \ufb01nd the percent.<\/p>\n<p>Answer:<br \/>\n28% of water in the 1st pool is greater than that of the smaller pool<\/p>\n<p>Explanation:<br \/>\nvolume of the first pool = 25 x 3 x 50=3750<br \/>\nvolume of the second pool = 25 x 21 x 2= 1050<br \/>\n1050 : 3750 = 0.28<br \/>\n0.28 = 28 %<br \/>\n<strong>Solve and Check<\/strong><br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Question 2.<br \/>\nUse a graph to represent the relationship between the surface area S(in square meters) and the height h(in meters) of the triangular prism. Then \ufb01nd the height when the surface area is 260 square meters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-303.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 303\" width=\"197\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the triangular prism = 43.33 meters<\/p>\n<p>Explanation:<br \/>\nThe surface area\u00a0 of the triangular prism = (1\/2) x b x h<br \/>\narea = (1\/2) x 12h<br \/>\n260 = 6h<br \/>\nh =(260\/6)<br \/>\nh = 43.33 m<\/p>\n<p>Question 3.<br \/>\nA toy company sells two different toy chests. The toy chests have different dimensions, but the same volume. What is the width w of Toy Chest 2?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26175\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-304.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 304\" width=\"295\" height=\"153\" \/><\/p>\n<p>Answer:<br \/>\nThe width of the toy chest2 = 384 in<\/p>\n<p>Explanation:<br \/>\nIn the above figure the toy chest 2 has length = 24 in and volume = 16 in<br \/>\nwidth = 24 x 16<br \/>\nwidth = 384 in<\/p>\n<p><strong>Performance Task<\/strong><br \/>\n<strong>Maximizing the Volumes of Boxes<\/strong><\/p>\n<p>At the beginning of this chapter, you watched a STEAM Video called \u201cPackaging Design.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-305.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 305\" width=\"282\" height=\"201\" \/><\/p>\n<h3>Area, Surface Area, and Volume Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the de\ufb01nition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-306.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 306\" width=\"630\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-306.png 630w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-306-300x41.png 300w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><\/p>\n<p>Answer:<br \/>\npolygon = a polygon is a closed figure in a plane that is made up of 3 or more line segments that intersect only at their endpoints.<br \/>\ncomposite figure = composite figure is made up of triangles, squares, rectangles and other two-dimensional figures.<br \/>\nkite = kite is a quadrilateral that has two pairs of adjacent sides with the same length and opposite sides with different lengths.<\/p>\n<p><strong>Graphic Organizers<\/strong><br \/>\nYou can use a Four Square to organize information about a concept. Each of the four squares can be a category, such as de\ufb01nition, vocabulary, example, non-example, words, algebra, table, numbers, visual, graph, or equation. Here is an example of a Four Square for the area of a parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-307.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 307\" width=\"463\" height=\"314\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-307.png 463w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-307-300x203.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><br \/>\n<strong>Choose and complete a graphic organizer to help you study the concept.<\/strong><\/p>\n<ol>\n<li>area of a triangle<\/li>\n<li>area of a trapezoid<\/li>\n<li>area of a composite \ufb01gure<\/li>\n<li>polyhedron<\/li>\n<li>surface area of a prism<\/li>\n<li>surface area of a pyramid<\/li>\n<li>volume of a rectangular prism<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-308.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 308\" width=\"280\" height=\"352\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-308.png 280w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-308-239x300.png 239w\" sizes=\"(max-width: 280px) 100vw, 280px\" \/><\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-309.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 309\" width=\"642\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-309.png 642w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-309-300x38.png 300w\" sizes=\"(max-width: 642px) 100vw, 642px\" \/><\/p>\n<p><strong>7.1 Areas of Parallelograms<\/strong> (pp. 285\u2013290)<\/p>\n<p>Find the area of the parallelogram.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-310.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 310\" width=\"165\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\narea = 500 yd<\/p>\n<p>Explanation:<br \/>\narea of the parallelogram = b x h<br \/>\narea = 25 x 20<br \/>\narea = 500 yd<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-311.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 311\" width=\"136\" height=\"142\" \/><\/p>\n<p>Answer:<br \/>\narea = 242 mm<\/p>\n<p>Explanation:<br \/>\narea of the parallelogram = b x h<br \/>\narea = 22 x 11<br \/>\narea = 242 mm<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-312.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 312\" width=\"158\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\narea = 45 cm<\/p>\n<p>Explanation:<br \/>\narea of the parallelogram = b x h<br \/>\narea = 9 x 5<br \/>\narea = 45 cm<\/p>\n<p>Question 4.<br \/>\nFind the area (in square inches) of the parallelogram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-313.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 313\" width=\"143\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\narea = 72 square in<\/p>\n<p>Explanation:<br \/>\narea of the parallelogram = b x h<br \/>\narea = 2 x 3<br \/>\narea = 6 ft<br \/>\n1 feet = 12 inches<br \/>\narea = 72 square inches<\/p>\n<p>Question 5.<br \/>\nThe billboard shown is in the shape of a parallelogram with a base of 48 feet. What is the height of the billboard?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-314.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 314\" width=\"317\" height=\"148\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-314.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-314-300x140.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the billboard = 14 ft<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = b x h<br \/>\n672 = 48 h<br \/>\nh = (672\/48)<br \/>\nh = 14 ft<\/p>\n<p>Question 6.<br \/>\nThe freeway noise barrier shown is made of identical parallelogram-shaped sections. The area of each section is 7.5 square meters, and the height of the barrier is 5 meters. How many meters wide is each section of the noise barrier?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-315.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 315\" width=\"307\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-315.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-315-300x181.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Answer:<br \/>\nEach section of the noise barrier is 1.5 m<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = b x h<br \/>\narea = 1.5 x5<br \/>\narea = 7.5<br \/>\nso b = 1.5 m<\/p>\n<p>Question 7.<br \/>\nDraw a parallelogram that has an area between 58 and 60 square centimeters.<\/p>\n<p>Answer:<br \/>\n59 square centimeters<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-50-1.png\" alt=\"\" width=\"204\" height=\"139\" \/><\/p>\n<p><strong>7.2 Areas of Triangles <\/strong>(pp. 291\u2013296)<\/p>\n<p>Find the area of the triangle.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-316.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 316\" width=\"199\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 80 sq. km<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = half the product of the base and the product of the height<br \/>\narea = (1\/2) x 16 x 10<br \/>\narea = (1\/2) x 160<br \/>\narea = 80 sq. km<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-317.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 317\" width=\"232\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 175 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = half the product of the base and the product of the height<br \/>\narea = (1\/2) x 14 x 25<br \/>\narea = (1\/2) x 350<br \/>\narea = 175 sq. cm<\/p>\n<p>Find the missing dimension of the triangle.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-318.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 318\" width=\"188\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nbase = 5 mi<\/p>\n<p>Explanation:<br \/>\nThe area of the tringle = b x h<br \/>\ngiven that h = 7 mi and area = 35 mi<br \/>\nbase = 5 mi<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-319.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 319\" width=\"158\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\nheight = 5 cm<\/p>\n<p>Explanation:<br \/>\nThe area of the tringle = b x h<br \/>\ngiven that b = 4 cm and area = 5 mi<br \/>\nheight = 5 cm<\/p>\n<p>Find the area of the figure.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-320.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 320\" width=\"187\" height=\"163\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 112.5 sq. yd<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (12 + 3). Given that b1 = 12 and b2 = 3<br \/>\narea = (1\/2) x 15(15) given that h = 15 yd<br \/>\narea = (1\/2) x 225<br \/>\narea = 112.5 sq. yd<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-321.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 321\" width=\"252\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 4 sq. mm<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (8 + 8). Given that b1 = 8 and b2 = 8<br \/>\narea = (1\/2) x 2(16) given that h = 2 yd<br \/>\narea = (1\/2) x 8<br \/>\narea = 4 sq. mm<\/p>\n<p>Question 14.<br \/>\nDraw a composite \ufb01gure that has an area of less than 35 square inches.<\/p>\n<p>Answer:<br \/>\nThe area of the triangle = b x h<br \/>\narea = 6 x 4<br \/>\narea = 24 square inches<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-51.png\" alt=\"\" width=\"291\" height=\"144\" \/><\/p>\n<p>Question 15.<br \/>\nTe triangle-shaped entrance to the cavern is 2\\([\\frac{1}{2}\/latex] feet tall and 4 feet wide. What is the area of the entrance?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-322.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 322\" width=\"199\" height=\"207\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the entrance = 10<\/p>\n<p>Explanation:<br \/>\n2 x(1\/2) = 5\/2 = 2.5<br \/>\n2.5 x 4 = 10<br \/>\n<strong>7.3 Areas of Trapezoids and Kites (pp. 297 &#8211; 304)<\/strong><\/p>\n<p>Question 16.<br \/>\nUse decomposition to \ufb01nd the area of the kite.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-323.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 323\" width=\"165\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-323.png 165w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-323-150x150.png 150w\" sizes=\"(max-width: 165px) 100vw, 165px\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the kite = 255 sq. in<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = (1\/2) x 10 x 9 + 10 x 21<br \/>\narea = (1\/2) x 90 +210<br \/>\narea = 45 + 210<br \/>\n255 sq. in<br \/>\n<strong>Find the area of the trapezoid.<\/strong><\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-324.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 324\" width=\"158\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 105 sq. m<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (15 + 6). Given that b1 = 15 and b2 = 6<br \/>\narea = (1\/2) x 10(21) given that h = 10 in<br \/>\narea = (1\/2) x 210<br \/>\narea = 105 sq. m<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-325.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 325\" width=\"116\" height=\"166\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 6 sq. in<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (1.5 + 2.5). Given that b1 = 1(1\/2) = 1.5 and b2 = 2(1\/2) = 2.5<br \/>\narea = (1\/2) x 3(4) given that h = 10 in<br \/>\narea = (1\/2) x 12<br \/>\narea = 6 sq. in<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-326.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 326\" width=\"172\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid =49 sq. mi<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (6 + 8). Given that b1 = 6 and b2 = 8<br \/>\narea = (1\/2) x 7(14) given that h = 7 mi<br \/>\narea = (1\/2) x 98<br \/>\narea = 49 sq. mi<\/p>\n<p>Find the area of the figure.<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-327.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 327\" width=\"124\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 56 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (6 + 7). Given that b1 = 6 and b2 = 7<br \/>\narea = (1\/2) x 8(14) given that h = 8 ft<br \/>\narea = (1\/2) x 112<br \/>\narea = 56 sq ft<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-328.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 328\" width=\"134\" height=\"187\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 48 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (4 + 8). Given that b1 = 4 and b2 = 8<br \/>\narea = (1\/2) x 8(12) given that h = 8 ft<br \/>\narea = (1\/2) x 96<br \/>\narea = 48 sq. cm<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-329.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 329\" width=\"190\" height=\"167\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid = 40 sq. in<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (6 +10). Given that b1 = 6 and b2 = 10<br \/>\narea = (1\/2) x 5(16) given that h = 80<br \/>\narea = (1\/2) x 80<br \/>\narea = 40 sq. in<\/p>\n<p>Question 23.<br \/>\nYou are creating a design for the side of the soapbox car. How much area do you have for the design?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-330.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 330\" width=\"249\" height=\"102\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid =240 sq. in<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (6 +14). Given that b1 = 6 and b2 = 14<br \/>\narea = (1\/2) x 24(20) given that h = 24<br \/>\narea = (1\/2) x 480<br \/>\narea = 240 sq. in<\/p>\n<p>Question 24.<br \/>\nFind the area (in square centimeters) of a trapezoid with a height of 2 meters and base lengths of 3 meters and 5 meters.<\/p>\n<p>Answer:<br \/>\nThe area of the trapezoid =240 sq. in<\/p>\n<p>Explanation:<br \/>\nThe area of the trapezoid = one half the product of its height h and the sum of its bases b1 and b2.<br \/>\narea = (1\/2) x h x( b1 + b2)<br \/>\narea =(1\/2) x h (3 +5). Given that b1 = 3 and b2 = 5<br \/>\narea = (1\/2) x 2(8) given that h = 2<br \/>\narea = (1\/2) x 16<br \/>\narea = 8 sq. m<br \/>\n1 meter = 100 cm<br \/>\narea = 8 x 100 = 800 sq. cm<\/p>\n<p><strong>7.4 Three-Dimensional Figures (pp. 305\u2013310)<\/strong><\/p>\n<p>Find the numbers of faces, edges, and vertices of the solid.<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-331.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 331\" width=\"113\" height=\"94\" \/><\/p>\n<p>Answer:<br \/>\nfaces = 6<br \/>\nedges = 12<br \/>\nvertices =7<\/p>\n<p>Explanation:<br \/>\nThe number of faces = 6<br \/>\nThe number of edges = 12<br \/>\nThe number of vertices =7<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-332.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 332\" width=\"128\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\nfaces = 5<br \/>\nedges = 10<br \/>\nvertices =6<\/p>\n<p>Explanation:<br \/>\nThe number of faces = 5<br \/>\nThe number of edges = 10<br \/>\nThe number of vertices =6<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-333.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 333\" width=\"95\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\nfaces = 9<br \/>\nedges = 20<br \/>\nvertices = 12<\/p>\n<p>Explanation:<br \/>\nThe number of faces = 9<br \/>\nThe number of edges = 20<br \/>\nThe number of vertices =12<\/p>\n<p>Draw the solid.<\/p>\n<p>Question 28.<br \/>\nsquare pyramid<\/p>\n<p>Answer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-31.jpg\" alt=\"\" width=\"116\" height=\"165\" \/><\/p>\n<p>Question 29.<br \/>\nhexagonal prism<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-32-300x258.png\" alt=\"\" width=\"300\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-32-300x258.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-32.png 318w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Draw the front, side, and top views of the solid.<\/strong><\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-334.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 334\" width=\"98\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\nfront = 1<br \/>\nside =2<br \/>\ntop = 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-52-300x56.png\" alt=\"\" width=\"300\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-52-300x56.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-52-768x143.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-52.png 795w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-335.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 335\" width=\"101\" height=\"104\" \/><\/p>\n<p>Answer:<br \/>\nfront = 4<br \/>\nside =2<br \/>\ntop = 2<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32493\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-54-300x52.png\" alt=\"\" width=\"300\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-54-300x52.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-54-768x133.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-54.png 801w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-336.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 336\" width=\"143\" height=\"100\" \/><\/p>\n<p>Answer:<br \/>\nfront = 1<br \/>\nside = 1<img loading=\"lazy\" class=\"alignnone size-medium wp-image-32492\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-53-300x59.png\" alt=\"\" width=\"300\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-53-300x59.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-53-768x150.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-53.png 827w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\ntop = 1<\/p>\n<p><strong>7.5 Surface Areas of Prisms (pp. 311\u2013318)<\/strong><\/p>\n<p><strong>Find the surface area of the prism.<\/strong><\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-26176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-7-Area-Surface-Area-and-Volume-337.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 337\" width=\"165\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the prism = 100 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 7 x 2 + 7 x 2 + 4x 7+ 4 x 7 + 4 x 2 + 4 x 2<br \/>\nsurface area = 14 +14+ 28 + 28 +8+8<br \/>\nsurface area = 100 sq. in<\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-338.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 338\" width=\"160\" height=\"114\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the prism = 243 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 6 x 9 + 6 x 9 + 9 x 4.5+ 9 x 4.5 + 6 x 4.5 + 6 x 4.5<br \/>\nsurface area = 54 +54+ 40.5 + 40.5 +27+ 27<br \/>\nsurface area = 243 sq. m<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-339.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 339\" width=\"133\" height=\"123\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the prism = 590 cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 8 x 7 + 8 x 7 + 15 x 8+ 15 x 8 + 17 x 7 + 17 x 7<br \/>\nsurface area = 56 +56+ 120 + 120 +119+ 119<br \/>\nsurface area = 590 sq. cm<\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-340.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 340\" width=\"144\" height=\"110\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the triangular prism = 49 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular prism = 2 b + p s<br \/>\nsurface area = 2 x 5 +6 x 6.5<br \/>\nsurface area = 10 + 39<br \/>\nsurface area = 49 sq. ft<\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-341.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 341\" width=\"134\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 1,17,649 cu. yd<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (7) x(7) x (7)<br \/>\nvolume = 49 x 49 x 49<br \/>\nvolume = 1,17,649 cu. yd<\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-342.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 342\" width=\"141\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 614.125 cu. mi<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh<br \/>\nwhere b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (17\/2) x(17\/2) x (17\/2)<br \/>\nvolume = 8.5 x 8.5 x 8.5<br \/>\nvolume = 614.125 cu. mi<\/p>\n<p>Question 39.<br \/>\nOne quart of water-resistant paint covers 75 square feet. A swimming pool is in the shape of a rectangular prism with a length of 20 feet, a width of 10 feet, and a height of 5 feet. How many quarts should you buy to paint the swimming pool with two coats of paint?<\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 1000 cu. ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular prism = b ase x height<br \/>\nvolume = b x h where b = l x w<br \/>\nvolume = 20 x 10 x 5<br \/>\nvolume = 1000 cu. ft<br \/>\n<strong>7.6 Surface Areas of Pyramids (pp. 319\u2013324)<\/strong><\/p>\n<p>Find the surface area of the pyramid.<\/p>\n<p>Question 40.<br \/>\nAn<\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-344.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 344\" width=\"114\" height=\"145\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the pyramid = 95.2 m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square pymarid = area + (1\/2) x ps<br \/>\nsurface area = 55.2 + (1\/2) x 10 x 8<br \/>\nsurface area = 55.2 + 40<br \/>\nsurface area = 95.2 m<\/p>\n<p>Question 42.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-345.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 345\" width=\"133\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the pyramid = 88.1 cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square pymarid = area + (1\/2) x ps<br \/>\nsurface area = 65.8 + (1\/2) x 7 x 9.4<br \/>\nsurface area = 55.2 + 32.9<br \/>\nsurface area = 88.1 cm<\/p>\n<p>Question 43.<br \/>\nYou make a square pyramid for a school project. Find the surface area of the pyramid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-346.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 346\" width=\"142\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the pyramid = 41.25<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square pyramid = area + (1\/2) x ps<br \/>\nsurface area = 27.5 + (1\/2) x 5.5 x 5<br \/>\nsurface area = 27.5 + 13.75<br \/>\nsurface area = 41.25 in<\/p>\n<p><strong>7.7 Volumes of Rectangular Prisms (pp. 325\u2013330)<\/strong><\/p>\n<p>Find volumes and missing dimensions of rectangular prisms.<\/p>\n<p>Question 44.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-347.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 347\" width=\"192\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 4.875 ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular prism = b ase x height<br \/>\nvolume = b x h where b = l x w<br \/>\nvolume = (5\/2) x (3\/2) x (4\/3)<br \/>\nvolume = 2.5 x 1.5 x 1.33<br \/>\nvolume = 4.875 ft<\/p>\n<p>Question 45.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-348.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 348\" width=\"111\" height=\"172\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 0.605 cm<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular prism = b ase x height<br \/>\nvolume = b x h where b = l x w<br \/>\nvolume = (1\/2) x (2\/3) x (11\/6)<br \/>\nvolume = 0.5 x 0.66 x 1.83<br \/>\nvolume = 0.605 cm<\/p>\n<p>Question 46.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-349.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 349\" width=\"142\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 0.05272 cu. in<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular prism = b ase x height<br \/>\nvolume = b x h where b = l x w<br \/>\nvolume = (3\/8) x (3\/8) x (3\/8)<br \/>\nvolume = 0.375 x 0.375 x 0.375<br \/>\nvolume = 0.05273 cu. in<\/p>\n<p>Question 47.<br \/>\nThe prism has a volume of 150 cubic feet. Find the length of the prism.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-350.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 350\" width=\"178\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nThe length of rectangular prism = 7 ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular prism = base x height<br \/>\nvolume = b x h where b = l x w<br \/>\nvolume = (5) x (4) x (7)<br \/>\nvolume = 150<br \/>\nlength = 7 ft<\/p>\n<p>Question 48.<br \/>\nHow many cubic inches of tissues can the box hold?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-351.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 351\" width=\"135\" height=\"149\" \/><\/p>\n<p>Answer:<br \/>\nThe length of rectangular prism = 162 . 5 in<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular prism = b ase x height<br \/>\nvolume = b x h where b = l x w<br \/>\nvolume = (5) x (5) x (6.5)<br \/>\nvolume = 162.5 in<\/p>\n<p>Question 49.<br \/>\nDraw a rectangular prism that has a volume less than 1 cubic inch.<\/p>\n<h3><a id=\"Area,_Surface_Area,_and_Volume_Practice_Test\"><\/a>Area, Surface Area, and Volume Practice Test<\/h3>\n<p><strong>7 Practice Test<\/strong><\/p>\n<p>Find the area of the \ufb01gure.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-352.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 352\" width=\"124\" height=\"100\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the parallelogram = 13000 cm<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = the product of the base and the product of the height<br \/>\narea = 130 x 100<br \/>\narea = 13000 cm<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-353.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 353\" width=\"141\" height=\"102\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 154 in<\/p>\n<p>Explanation:<br \/>\nThe area of the triangle = (1\/2 ) x b x h<br \/>\narea = (1\/2) x 14 x 22<br \/>\narea = (1\/2) x 308<br \/>\narea = 154 in<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-354.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 354\" width=\"165\" height=\"131\" \/><\/p>\n<p><strong>Find the surface area of the solid.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-355.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 355\" width=\"195\" height=\"102\" \/><\/p>\n<p>Answer:<br \/>\n340\u00a0 ft<\/p>\n<p>Explanation:<br \/>\nSurface area = area of the bottom + area of the front +area of the back +area of a side + area of a side<br \/>\nsurface area = 12 x 7 = 84+ (1\/2) x 7 x 5 = 17.5+ (1\/2) x\u00a0 7 x 5 = 17.5+\u00a0 13 x 5 = 65 + 12 x 13\u00a0 = 156<br \/>\nbottom = 12 x 7 , front = (1\/2) x 7 x 5, back = (1\/2) x 7 x 5, side = 13 x 5 , side = 12 x 13<br \/>\nsurface\u00a0 area = 84 + 17.5 +17.5 + 65+156<br \/>\narea = 340 ft<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-356.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 356\" width=\"120\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism =1567.5 m<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = Bh where b = l x w<br \/>\nwhere b = area of the base<br \/>\nvolume = (9.5) x(11) x (15)<br \/>\nvolume = 1567.5 m<\/p>\n<p>Find the volume of the prism.<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-357.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 357\" width=\"117\" height=\"122\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 3.5 cm<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = b x h<br \/>\nvolume = (3\/2) x (7\/3)<br \/>\nvolume = 1.5 x 2.33<br \/>\nvolume = 3.5 cm<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-358.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 358\" width=\"120\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the prism = 0.64 yd<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = b x h<br \/>\nvolume = (4\/5) x (4\/5)<br \/>\nvolume = 0.8 x 0.8<br \/>\nvolume = 0.64 yd<\/p>\n<p>Question 8.<br \/>\nDraw an octagonal prism.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-volumes-chapter-7-4.2-39.png\" alt=\"\" width=\"171\" height=\"169\" \/><\/p>\n<p>Question 9.<br \/>\nFind the numbers of faces, edges, and vertices of the solid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-359.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 359\" width=\"82\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nfaces = 8<br \/>\nedges = 26<br \/>\nvertices = 10<\/p>\n<p>Explanation:<br \/>\nThe number of faces = 8<br \/>\nthe number of edges = 26<br \/>\nthe number of vertices = 10<\/p>\n<p>Question 10.<br \/>\nThe area of a parallelogram is 156 square meters. What is the height of the parallelogram when the base is 13 meters?<\/p>\n<p>Answer:<br \/>\nThe base of the parallelogram = 12 square meters<\/p>\n<p>Explanation:<br \/>\nThe area of the parallelogram = b x h<br \/>\narea = 13 x\u00a0 12<br \/>\narea = 156<br \/>\nso base = 12 square meters<\/p>\n<p>Question 11.<br \/>\nA candle is shaped like a square pyramid. Find the surface area of the candle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-360.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 360\" width=\"114\" height=\"99\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the candle = 21.6 in<\/p>\n<p>Explanation:<br \/>\nThe area of the square pyramid = area +(1\/2) x p x s<br \/>\nsurface area = 14.4 +(1\/2) x 4 x 3.6<br \/>\nsurface area = 14.4 + 7.2<br \/>\nsurface area = 21.6 in<\/p>\n<p>Question 12.<br \/>\nYou are wrapping the boxed DVD collection as a present. What is the least amount of wrapping paper needed to wrap the box?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-361.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 361\" width=\"214\" height=\"153\" \/><\/p>\n<p>Question 13.<br \/>\nA cube has an edge length of 4 inches. You double the edge lengths. How many times greater is the volume of the new cube?<\/p>\n<p>Answer:<br \/>\n2 times greater<\/p>\n<p>Explanation:<br \/>\nGiven that the cube has an edge length of 4 inches<br \/>\nThey said to double the cube<br \/>\n4 x 2 = 8<br \/>\nthe volume of the new cube is 2 times greater than that of the old cube<\/p>\n<p>Question 14.<br \/>\nThe Pentagon in Arlington, Virginia, is the headquarters of the U.S. Department of Defense. The building\u2019s center contains a pentagon-shaped courtyard with an area of about 5 acres. Find the land areas (in square feet) of the courtyard and the building.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-362.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 362\" width=\"235\" height=\"230\" \/><\/p>\n<h3><a id=\"Area,_Surface_Area,_and_Volume_Cumulative_Practice\"><\/a>Area, Surface Area, and Volume Cumulative Practice<\/h3>\n<p><strong>7 Cumulative Practice<\/strong><\/p>\n<p>Question 1.<br \/>\nA cruise ship is carrying a total of 4971 people. Each life boat can hold a maximum of 150 people. What is the minimum number of lifeboats needed to evacuate everyone on the cruise ship?<br \/>\nA. 33 lifeboats<br \/>\nB. 34 lifeboats<br \/>\nC. 54 lifeboats<br \/>\nD. 332 lifeboats<\/p>\n<p>Answer:<br \/>\noption A is correct<\/p>\n<p>Explanation:<br \/>\n150\/33 = 4971 boats<br \/>\nIn the above question, the lifeboat can hold a maximum of 150 people<br \/>\nThe minimum no of lifeboats needed = 33<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-25952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-363.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 363\" width=\"327\" height=\"401\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-363.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-363-245x300.png 245w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><\/p>\n<p>Question 2.<br \/>\nWhich number is equivalent to the expression?<br \/>\n3 . 4<sup>2<\/sup> + 6 \u00f7 2<br \/>\nF. 27<br \/>\nG. 33<br \/>\nH. 51<br \/>\nI. 75<\/p>\n<p>Answer:<br \/>\noption H is correct<\/p>\n<p>Explanation:<br \/>\n3 . 16 + 3<br \/>\n48 + 3<br \/>\n51<br \/>\nQuestion 3.<br \/>\nWhat is the volume of the package?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-364.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 364\" width=\"374\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-364.png 374w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-364-300x210.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><\/p>\n<p>Question 4.<br \/>\nA housing community started with 60 homes. In each of the following years, 8 more homes were built. Let represent the number of years that have passed since the \ufb01rst year, and let n represent the number of homes. Which equation describes the relationship between n and y?<br \/>\nF. n = 8y + 60<br \/>\nG. n = 68y<br \/>\nH. n = 60y + 8<br \/>\nI. n = 60 + 8 + y<\/p>\n<p>Answer:<br \/>\noption I is the correct<\/p>\n<p>Explanation:<br \/>\nn = 60 + 8 + y<br \/>\nwhere n = no of homes<br \/>\ny = number of years<\/p>\n<p>Question 5.<br \/>\nWhat is the value of m that makes the equation true?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-365.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 365\" width=\"90\" height=\"73\" \/><\/p>\n<p>4m = 6<\/p>\n<p>Answer:<br \/>\nthe value of m = (6\/4)<\/p>\n<p>Explanation:<br \/>\nm = (6\/4)<br \/>\n4m = 6<br \/>\n4 x (6\/4) = 6<br \/>\n6 = 6<\/p>\n<p>Question 6.<br \/>\nWhat is the surface area of the square pyramid?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-366.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 366\" width=\"376\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-366.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-366-300x189.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p>Answer:<br \/>\nnone of the options are correct<\/p>\n<p>Explanation:<br \/>\nsurface area of the pyramid = area +(1\/2)x(5x 3)<br \/>\narea = 15+ (1\/2) (15)<br \/>\narea = 15 + 7.5<br \/>\narea = 22.5 in<br \/>\nQuestion 7.<br \/>\nA wooden box has a length of 12 inches, a width of 6 inches, and a height of 8 inches.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-367.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 367\" width=\"76\" height=\"86\" \/><br \/>\n<strong>Part A<\/strong><br \/>\nDraw and label a rectangular prism with the dimensions of the wooden box.<br \/>\n<strong>Part B<\/strong><br \/>\nWhat is the surface area, in square inches, of the wooden box? Show your work.<br \/>\n<strong>Part C<\/strong><br \/>\nYou have a two-\ufb02uid ounce sample of wood stain that covers 900 square inches. Is this enough to give the entire box two coats of stain? Show your work and explain your reasoning.<\/p>\n<p>Answer:<br \/>\nThe surface area of the rectangular prism = 432 in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = Area of the top + area of the bottom +area of front + area of back + area of side + area of a side<br \/>\nsurface area = 12 x 6 + 12 x 6 + 6 x 8 + 6 x 8 + 12 x 8+ 12 x 8<br \/>\nsurface area = 72+ 72 + 48 + 48 + 96 +96<br \/>\nsurface area = 432 in<br \/>\na : <img loading=\"lazy\" class=\"alignnone size-full wp-image-32494\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-6-chapter-7.2-lesson-4-55.png\" alt=\"\" width=\"278\" height=\"157\" \/><\/p>\n<p>Question 8.<br \/>\nOn Saturday, you earned $35 mowing lawns. This was dollars more than you earned on Thursday. Which expression represents the amount, in dollars, you earned mowing lawns on Thursday?<br \/>\nF. 35x<br \/>\nG. x + 35<br \/>\nH. x &#8211; 35<br \/>\nI. 35 &#8211; x<\/p>\n<p>Answer:<br \/>\nOption G is correct<\/p>\n<p>Explanation:<br \/>\nx + 35 is correct<\/p>\n<p>Question 9.<br \/>\nWhat is the area, in square yards, of the triangle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-368.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 368\" width=\"298\" height=\"170\" \/><\/p>\n<p>Answer:<br \/>\nThe area of the triangle = 20 yd<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = (1\/2) x b x h<br \/>\narea = (1\/2) x 5 x 8 where b = 5 and h = 8 given<br \/>\narea = (1\/2) x 40<br \/>\narea = 20yd<\/p>\n<p>Question 10.<br \/>\nWhich expression is equivalent to [latex]\\frac{12}{35}\\) ?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-369.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 369\" width=\"347\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-369.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-369-300x94.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Answer:<br \/>\noption b is correct<\/p>\n<p>Explanation:<br \/>\n(2 x 6)\/(7 x 5)<br \/>\n12 \/ 35<br \/>\nso option b is correct<br \/>\nQuestion 11.<br \/>\nThe description below represents the area of which polygon?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-370.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 370\" width=\"429\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-370.png 429w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-370-300x44.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><br \/>\nF. rectangle<br \/>\nG. parallelogram<br \/>\nH. trapezoid<br \/>\nI. triangle<\/p>\n<p>Answer:<br \/>\noption h is correct<\/p>\n<p>Explanation:<br \/>\nThe formula of trapezoid = 0ne half the product of its height and the sum of its bases.<\/p>\n<p>Question 12.<br \/>\nWhat is the missing quantity in the double number line?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-25962\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-7-Area-Surface-Area-and-Volume-371.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 7 Area, Surface Area, and Volume 371\" width=\"287\" height=\"112\" \/><br \/>\nA. 25 ounces<br \/>\nB. 165 ounces<br \/>\nC. 525 ounces<br \/>\nD. 600 ounces<\/p>\n<p>Answer:<br \/>\nOption b is correct<\/p>\n<p>Explanation:<br \/>\n6 + 15 = 21<br \/>\n150 + 15 = 165<br \/>\nso option b is correct<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>We wish the information mentioned in the above sections will help you in your preparation. You can get the free links to download Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume pdf. Practice all the problems available in the above links and also share it with your friends and peers. You can overcome all the difficulties in grade 6 maths. Moreover, bookmark our page to get the solutions of all Big Ideas Math Grade 6 Chapters.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Wanna get the best preparatory material of Big Ideas Math 6th Grade Chapters? If yes, then you have hit the exact page. Here, in this article, we are providing in-depth concepts of area, surface area, and volume. You can understand all the concepts with the help of Big Ideas Math Book Solutions. We are providing &#8230; <a title=\"Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6-chapter-7\/\" aria-label=\"More on Big Ideas Math Answers Grade 6 Chapter 7 Area, Surface Area, and Volume\">Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":89720,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/04\/Big-Ideas-Math-Answers-Grade-6-Chapter-7-Area-Surface-Area-and-Volume.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/25610"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=25610"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/25610\/revisions"}],"predecessor-version":[{"id":90339,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/25610\/revisions\/90339"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89720"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=25610"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=25610"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=25610"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}