{"id":78090,"date":"2021-03-27T21:31:43","date_gmt":"2021-03-27T16:01:43","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=78090"},"modified":"2022-04-01T10:27:17","modified_gmt":"2022-04-01T04:57:17","slug":"eureka-math-grade-7-module-3-lesson-19","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/eureka-math-grade-7-module-3-lesson-19\/","title":{"rendered":"Eureka Math Grade 7 Module 3 Lesson 19 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 7th Grade Module 3 Lesson 19 Answer Key<\/h2>\n

Eureka Math Grade 7 Module 3 Lesson 19 Example Answer Key<\/h3>\n

Example: Area of a Parallelogram
\nThe coordinate plane below contains figure P, parallelogram ABCD.
\n\"Engage
\nAnswer:
\n\"Engage
\na. Write the ordered pairs of each of the vertices next to the vertex points.
\nAnswer:
\nSee figure.<\/p>\n

b. Draw a rectangle surrounding figure P that has vertex points of A and C. Label the two triangles in the figure as S and T.
\nAnswer:
\nSee figure.<\/p>\n

c. Find the area of the rectangle.
\nAnswer:
\nBase = 8 units
\nHeight = 6 units
\nArea = 8 units \u00d7 6 units = 48 sq. units<\/p>\n

d. Find the area of each triangle.
\nAnswer:
\nFigure S
\nBase = 3 units
\nHeight = 6 units
\nArea = \\(\\frac{1}{2}\\) \u00d7 3 units \u00d7 6 units
\n= 9 sq. units
\nFigure T
\nBase = 3 units
\nHeight = 6 units
\nArea = \\(\\frac{1}{2}\\) \u00d7 3 units \u00d7 6 units
\n= 9 sq. units<\/p>\n

e. Use these areas to find the area of parallelogram ABCD.
\nAnswer:
\nArea P = Area of rectangle – Area S – Area T
\n= 48 sq. units – 9 sq. units – 9 sq. units = 30 sq. units<\/p>\n

The coordinate plane below contains figure R, a rectangle with the same base as the parallelogram above.
\n\"Engage
\nAnswer:
\n\"Engage
\nf. Draw triangles S and T and connect to figure R so that you create a rectangle that is the same size as the rectangle you created on the first coordinate plane.
\nAnswer:
\nSee figure.<\/p>\n

g. Find the area of rectangle R.
\nAnswer:
\nBase = 5 units
\nHeight = 6 units
\nArea = 30 sq. units<\/p>\n

h. What do figures R and P have in common?
\nAnswer:
\nThey have the same area. They share the same base and have the same height.<\/p>\n

Eureka Math Grade 7 Module 3 Lesson 19 Exercise Answer Key<\/h3>\n

Exercise 1.
\nFind the area of triangle ABC.
\n\"Engage
\nAnswer:
\nA = \\(\\frac{1}{2}\\) \u00d7 7 units \u00d7 4 units = 14 sq.units<\/p>\n

Exercise 2.
\nFind the area of quadrilateral ABCD two different ways.
\n\"Engage
\nAnswer:
\n\"Engage
\n\\(\\frac{1}{2}\\) \u00d7 2 \u00d7 5 + 2 \u00d7 5 + \\(\\frac{1}{2}\\) \u00d7 1 \u00d7 5 = 5 + 10 + 2.5 = 17.5
\nThe area is 17.5 sq.units.<\/p>\n

\"Engage
\n\\(\\frac{1}{2}\\) \u00d7 (5 + 2) \u00d7 5 = 17.5
\nThe area is 17.5 sq.units.<\/p>\n

Exercise 3.
\nThe area of quadrilateral ABCD is 12 sq. units. Find x.
\n\"Engage
\nAnswer:
\nArea = base\u00d7height
\n12 sq.units = 2x
\n6 units = x<\/p>\n

Exercise 4.
\nThe area of triangle ABC is 14 sq. units. Find the length of side \\(\\overline{B C}\\).
\n\"Engage
\nAnswer:
\nArea = \\(\\frac{1}{2}\\) \u00d7 base\u00d7height
\n14 sq.units = \\(\\frac{1}{2}\\) \u00d7 BC \u00d7 (7 units)
\nBC = 4 units<\/p>\n

Exercise 5.
\nFind the area of triangle ABC.
\n\"Engage
\nAnswer:
\nArea of rectangle ARST = 11 units \u00d7 10 units = 110 sq.units
\nArea of triangle ARB = \\(\\frac{1}{2}\\) \u00d7 7 units\u00d710 units = 35 sq.units
\nArea of triangle BSC = \\(\\frac{1}{2}\\) \u00d7 4 units\u00d75 units = 10 sq.units
\nArea of triangle ATC = \\(\\frac{1}{2}\\) \u00d7 11 units\u00d75 units = 27.5 sq.units
\nArea of triangle ABC = Area of ARST – Area of ARB – Area of BSC – Area of ATC = 37.5 sq.units<\/p>\n

Eureka Math Grade 7 Module 3 Lesson 19 Problem Set Answer Key<\/h3>\n

Find the area of each figure.
\nQuestion 1.
\n\"Eureka
\nAnswer:
\nArea = 13.5 sq. units<\/p>\n

Question 2.
\n\"Eureka
\nAnswer:
\nArea = 4.5\u03c0 sq. units \u224814.13 sq. units<\/p>\n

Question 3.
\n\"Eureka
\nAnswer:
\nArea = 48 sq. units<\/p>\n

Question 4.
\n\"Eureka
\nAnswer:
\nArea = (2\u03c0 + 16) sq. units \u2248 22.28 sq. units<\/p>\n

Question 5.
\n\"Eureka
\nAnswer:
\nArea = 68 sq. units<\/p>\n

Question 6.
\n\"Eureka
\nAnswer:
\nArea = 46 sq. units<\/p>\n

For Problems 7\u20139, draw a figure in the coordinate plane that matches each description.
\nQuestion 7.
\nA rectangle with an area of 18 sq. units
\n\"Eureka
\nAnswer:
\n\"Eureka<\/p>\n

Question 8.
\nA parallelogram with an area of 50 sq. units
\n\"Eureka
\nAnswer:
\n\"Eureka<\/p>\n

Question 9.
\nA triangle with an area of 25 sq. units
\n\"Eureka
\nAnswer:
\n\"Eureka<\/p>\n

Find the unknown value labeled as x on each figure.
\nQuestion 10.
\nThe rectangle has an area of 80 sq. units.
\n\"Eureka
\nAnswer:
\nx = 8<\/p>\n

Question 11.
\nThe trapezoid has an area of 115 sq. units.
\n\"Eureka
\nAnswer:
\nx = 10<\/p>\n

Question 12.
\nFind the area of triangle ABC.
\n\"Eureka
\nAnswer:
\nArea = 6.5 sq. units<\/p>\n

Question 13.
\nFind the area of the quadrilateral using two different methods. Describe the methods used, and explain why they result in the same area.
\n\"Eureka
\nAnswer:
\nArea = 15 sq. units
\nOne method is by drawing a rectangle around the figure. The area of the parallelogram is equal to the area of the rectangle minus the area of the two triangles. A second method is to use the area formula for a parallelogram (Area = base \u00d7 height).<\/p>\n

Question 14.
\nFind the area of the quadrilateral using two different methods. What are the advantages or disadvantages of each method?
\n\"Eureka
\nAnswer:
\nArea = 60 sq. units
\nOne method is to use the area formula for a trapezoid, A = \\(\\frac{1}{2}\\) (base 1 + base 2)\u00d7height. The second method is to split the figure into a rectangle and a triangle. The second method requires more calculations. The first method requires first recognizing the figure as a trapezoid and recalling the formula for the area of a trapezoid.<\/p>\n

Eureka Math Grade 7 Module 3 Lesson 19 Exit Ticket Answer Key<\/h3>\n

The figure ABCD is a rectangle. AB = 2 units, AD = 4 units, and AE = FC = 1 unit.
\n\"Eureka
\nQuestion 1.
\nFind the area of rectangle ABCD.
\nAnswer:
\nArea = 4 units \u00d7 2 units = 8 sq. units<\/p>\n

Question 2.
\nFind the area of triangle ABE.
\nAnswer:
\nArea = \\(\\frac{1}{2}\\) \u00d7 1 unit \u00d7 2 units = 1 sq. unit<\/p>\n

Question 3.
\nFind the area of triangle DCF.
\nAnswer:
\nArea = \\(\\frac{1}{2}\\) \u00d7 1 unit \u00d7 2 units = 1 sq. unit<\/p>\n

Question 4.
\nFind the area of the parallelogram BEDF two different ways.
\nAnswer:
\nArea = Area of ABCD \u2013 Area of ABE \u2013 Area of DCF
\n= (8 – 1 – 1) sq. units = 6 sq. units<\/p>\n

Area = base \u00d7 height
\n= 3 units \u00d7 2 units = 6 sq. units<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 7th Grade Module 3 Lesson 19 Answer Key Eureka Math Grade 7 Module 3 Lesson 19 Example Answer Key Example: Area of a Parallelogram The coordinate plane below contains figure P, parallelogram ABCD. Answer: a. Write the ordered pairs of each of the vertices next to the vertex points. Answer: See … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/78090"}],"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\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=78090"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/78090\/revisions"}],"predecessor-version":[{"id":92011,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/78090\/revisions\/92011"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=78090"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=78090"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=78090"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}