The success criteria of Find Perimeter and Area is to understand the area and perimeter of polygons. The topic wise quick links to access Big Ideas Math Book Grade 3 Chapter 15 Find Perimeter and Area Answer Key is provided below. So, just tap on them and get the solutions easily.<\/p>\n
Lesson 1 Understand Perimeter<\/strong><\/p>\n Lesson 2 Find Perimeters of Polygons<\/strong><\/p>\n Lesson 3 Find Unknown Side Lengths Lesson 4 Same Perimeter, Different Areas<\/strong><\/p>\n Lesson 5 Same Area, Different Perimeters<\/strong><\/p>\n Performance Task Explore and Grow<\/strong><\/p>\n Question 1. Explanation: Structure<\/strong> Answer: Explanation: Think and Grow: Understand Perimeter<\/strong> Explanation: Show and Grow<\/strong><\/p>\n Question 1. Explanation: Question 2. Explanation: Question 3. Explanation: Apply and Grow: Practice<\/strong><\/p>\n Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Explanation: Question 10. Explanation: Think and Grow: Modeling Real Life<\/strong> Explanation: Show and Grow<\/strong><\/p>\n Question 11. Explanation: Question 12. Explanation: Question 13. Question 1. Explanation: Question 2. Answer: Explanation: Question 3. Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Review & Refresh<\/strong><\/p>\n Write two equivalent fractions for the whole number.<\/p>\n Question 9. Explanation: Question 10. Explanation: Question 11. Explanation: Explore and Grow<\/strong><\/p>\n Model a rectangle on your geoboard. Draw the rectangle and label its side lengths. Then \ufb01nd the perimeter in more than one way. Answer: Explanation: Explanation: Think and Grow: Find Perimeter<\/strong><\/p>\n Example Explanation: Example Answer: Explanation: Show and Grow<\/strong><\/p>\n Find the perimeter of the polygon. Explanation: Question 1. Explanation: Question 2. Answer: Explanation: Apply and Grow: Practice<\/strong><\/p>\n Find the perimeter of the polygon.<\/p>\n Question 3. Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Explanation: Question 10. Explanation: So to find the perimeter\u00a0of the trapezoid is we will add the length of all sides. Question 11. Explanation: Question 12. Explanation: Think and Grow: Modeling Real Life<\/strong><\/p>\n The rectangular sign is 34 feet longer than it is wide. What is the perimeter of the sign? Explanation: Show and Grow<\/strong><\/p>\n Question 13. Explanation: Question 14. Explanation: Question 15. Explanation: Find the perimeter of the polygon<\/p>\n Question 1. Explanation: Question 2. Explanation: Question 3. Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Explanation: Question 10. Explanation: Question 11. Explanation: Review & Refresh<\/strong><\/p>\n Question 12. Explanation: Question 13. Explanation: Question 14. Explanation: Explore and Grow<\/strong><\/p>\n You have a map with the three side lengths shown. The perimeter of the map is 20 feet. Describe how you can \ufb01nd the fourth side length of your map without measuring. Answer: Explanation: Repeated Reasoning<\/strong> Explanation: Think and Grow: Find Unknown Side Lengths<\/strong> Explanation: Example Explanation: Show and Grow<\/strong><\/p>\n Find the unknown side length.<\/p>\n Question 1. Explanation: Question 2. Explanation: Apply and Grow: Practice<\/strong><\/p>\n Find the unknown side length.<\/p>\n Question 3. Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Explanation: Question 10. Explanation: Question 11. Explanation: Think and Grow: Modeling Real Life<\/strong><\/p>\n The perimeter of the rectangular vegetable garden is 30 meters. What are the lengths of the other three sides? Explanation: Show and Grow<\/strong><\/p>\n Question 12. Explanation: Question 13. Explanation: Question 14. Explanation: Find the unknown side length.<\/p>\n Question 1. Explanation: Question 2. Explanation: Question 3. Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Explanation: Question 10 Explanation: Review & Refresh<\/strong><\/p>\n Write the time. Write another way to say the time.<\/p>\n Question 11. Explanation: Question 12. Explanation: Question 13. Explanation: Use color tiles to create two different rectangles that each have a perimeter of 16 units. Then draw your rectangles and label their dimensions. Do the rectangles have the same area? Explain how you know. Answer: Explanation:<\/p>\n Repeated Reasoning<\/strong> Explanation: Think and Grow : Same Perimeter, Different Areas<\/strong><\/p>\n Example :<\/strong> Explanation: we can see in the above figure another rectangle with a length of 8m, Show and Grow<\/strong><\/p>\n Question 1. Explanation: we can see in the above figure another rectangle with a length of 4 in, Apply and Grow: Practice<\/strong><\/p>\n Find the perimeter and area of Rectangle A. Draw a different rectangle that has the same perimeter. Which rectangle has the greater area?<\/p>\n Question 2. Explanation: we can see in the above figure another rectangle with a length of 6 cm, Question 3. Rectangle B Explanation: we can see in the above figure another rectangle with a length of 6 m, Question 4. Answer: Explanation: we can see in the above figure another rectangle with a length of 10 ft, Think and Grow: Modeling Real Life<\/strong><\/p>\n A paleontologist has 12 meters of twine to rope off a rectangular section of the ground. How long and wide should she make the roped-off section so it has the greatest possible area? Explanation: Show and Grow<\/strong><\/p>\n Question 5. Explanation: Question 6. Descartes also builds a fort. He has the same length of rope as you to make a perimeter around his fort. Descartes\u2019s roped-off section has a lesser area than yours. Draw one way Descartes could rope off his fort.<\/p>\n Answer: Explanation: Let the length of the Descarte’s rope is 8 ft Question 1. Explanation: we can see in the above figure rectangle with a length of 6.5 cm, Question 2. Explanation: Question 3. Explanation: Question 4. The school builds another playground. It has the same perimeter as the \ufb01rst. The third playground has a greater area than the \ufb01rst. Draw one way the third playground could look Explanation:\n
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<\/a>Lesson 15.1 Understand Perimeter<\/h3>\n
\nModel a rectangle on your geoboard. Draw the rectangle and label its side lengths. What is the distance around the rectangle?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-15-Find-Perimeter-and-Area-1.png\")
\nAnswer:
\nThe units around the rectangle are 15 units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-4.png\")
\nIn the above figure, the length of the rectangle is 4 units, and
\nthe breadth of the rectangle is 3 units.
\nThe units around the rectangle are 15 units.<\/p>\n
\nChange the side lengths of the rectangle on your geoboard. What do you notice about the distance around your rectangle compared to the distance around the rectangle above? Explain<\/p>\n
\nThe distance around the rectangle is 15 units<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-4-1.png\")
\nIn the above figure, we can see the length of the rectangle is 3 units, and
\nthe breadth of the rectangle is 4 units.
\nThere is no change in the distance around the rectangle which is 15 units.<\/p>\n
\nPerimeter is the distance around a \ufb01gure. You can measure perimeter using standard units, such as inches, feet, centimeters, and meters.
\nExample<\/strong>
\nFind the perimeter of the rectangle.
\nChoose a unit to begin counting. Count each unit around the rectangle.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-2.png\")
\nAnswer:
\nThe perimeter of the rectangle is 20 in.<\/p>\n
\nTo find the perimeter of the triangle, we need to know the length and the breadth of the rectangle.
\nHere, the length of the rectangle is 7 in,
\nand the breadth is 3 in,
\nSo the perimeter of the rectangle is 2(Length + Breadth)
\n= 2(7+3)
\n= 2(10)
\n= 20 in.<\/p>\n
\nFind the perimeter of the figure.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-4.png\")
\nThere are ___ units around the figure.
\nAnswer:
\nThere are 22 units around the figure.<\/p>\n
\nTo find the perimeter of the rectangle, we need to know the length and the breadth of the rectangle.
\nHere, the length of the rectangle is 6 m,
\nand the breadth is 5 m,
\nSo the perimeter of the rectangle is 2(Length + Breadth)
\n= 2(6+5)
\n= 2(11)
\n= 22 m.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-5.png\")
\nThere are ___ units around the figure.
\nSo, the perimeter is ____ feet.
\nAnswer:
\nThe perimeter of the figure is 24 ft.<\/p>\n
\nTo find the perimeter of the figure, we will add all the sides of the figure
\nSo the sides of the figure are 5,3,2,4,3,7.
\nand the perimeter of the figure is 5+3+2+4+3+7
\n= 24 ft.<\/p>\n
\nDraw the figure that has a perimeter of 16 centimeters.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-6.png\")
\nAnswer:
\nThe sides of the figure are 4 cm.<\/p>\n
\nAs the perimeter of the figure is 16 cm,
\nSo let the sides of the figure be 4 cm,
\nby that, we can get the perimeter as 16 cm, i.e
\n4+4+4+4= 16 cm.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-1-300x208.png\")
<\/p>\n
\nFind the perimeter of the \ufb01gure.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-7.png\")
\nThere are ___ units around the figure.
\nSo, the perimeter is ___
\nAnswer:
\nThere are 20 units around the figure.
\nSo, the perimeter is 20 cm.<\/p>\n
\nTo find the perimeter of the figure, we will add all the sides of the figure
\nSo the sides of the figure are 3,3,2,2,5,5.
\nand the perimeter of the figure is 3+3+2+2+5+5
\n= 20 units,
\nSo the perimeter is 20 cm.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-8.png\")
\nThere are ___ units around the figure.
\nSo, the perimeter is ___
\nAnswer:
\nThere are 26 units around the figure.
\nSo, the perimeter is 26 ft.<\/p>\n
\nTo find the perimeter of the figure, we will add all the sides of the figure
\nSo the sides of the figure is 5,5,2,3,1,3,2,5
\nand the perimeter of the figure is 5+5+2+3+1+3+2+5
\n= 26 units,
\nSo the perimeter is 26 ft.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-9.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the figure is 22 in.<\/p>\n
\nTo find the perimeter of the figure, we will add all the sides of the figure
\nSo the sides of the figure is 4,3,2,3,3,3,1,3
\nand the perimeter of the figure is 4+3+2+3+3+3+1+3
\n= 22 units,
\nSo the perimeter is 22 in.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-10.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter is 24 m.<\/p>\n
\nTo find the perimeter of the figure, we will add all the sides of the figure
\nSo the sides of the figure is 5,7,2,2,1,2,1,1,1,2
\nand the perimeter of the figure is 5+7+2+2+1+2+1+1+1+2
\n= 24 units,
\nSo the perimeter is 24 m.<\/p>\n
\nDraw a \ufb01gure that has a perimeter likely measurement for the of 14 centimeters.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-11.png\")
\nAnswer:
\nThe length of the rectangle is 2 cm, and
\nthe breadth is 5 cm.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Screenshot-529.png\")
\nIn the above figure, we can see the length of the rectangle is 2 cm
\nand the breadth of the rectangle is 5 cm
\nperimeter = 2(length + breadth)
\n= 2(5+2)
\n= 2(7)
\n= 14 cm.
\nso the perimeter of the rectangle is 14 cm.<\/p>\n
\nPrecision<\/strong> Which is the most likely measurement for the perimeter of a photo?
\n20 inches
\n100 meters
\n5 centimeters
\n2 inches
\nAnswer:
\n2 inches.<\/p>\n
\nThe most likely measurement for the perimeter of a photo is 2 inches.<\/p>\n
\nYou be the teacher<\/strong> Your friend counts the units around the figure and says the perimeter is 12 units. Is your friend correct? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-12.png\")
\nAnswer:
\nNo, he is not correct.<\/p>\n
\nNo, he is not correct. As there are 2+2+1+1+4+1+1+2= 14 units, but not 12 units. So he is not correct.<\/p>\n
\nUse a centimeter ruler to \ufb01nd the perimeter of the bookmark.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-13.png\")
\nThe perimeter is ___
\nAnswer:
\nThe perimeter of the bookmark is 26 cm.<\/p>\n
\nOn measuring, the length of the sides of the bookmark are 4 cm, 9 cm, 2 cm, 2 cm, 9 cm
\nto find the perimeter of the bookmark, we will add all the length of the sides
\nso the perimeter of the bookmark is
\np = 4 cm+ 9 cm+ 2 cm+ 2 cm+ 9 cm
\n= 26 cm.
\nThe perimeter of the bookmark is 26 cm.<\/p>\n
\nUse an inch ruler to find the perimeter of the decal.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-14.png\")
\nAnswer:
\nThe perimeter of the decal is 17 in.<\/p>\n
\nOn measuring, the length of the sides of the decal is 5in, 2in, 5in, 5in
\nto find the perimeter of the decal, we will add all the length of the sides
\nso the perimeter of the decal is
\np= 5in+2in+5in+5in
\n= 17 in
\nThe perimeter of the decal is 17 in.<\/p>\n
\nHow much greater is the perimeter of your friend\u2019s desk than the perimeter of your desk?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-15.png\")
\nAnswer:
\nFriend’s perimeter is 22-16= 6 times greater.<\/p>\n
\nAs we can see figure 1 is a square and the sides of the square are 4 ft.
\nSo the perimeter of the square is a+a+a+a,
\n= 4+4+4+4
\n= 16 ft.
\nAnd now let’s find the perimeter of the friend’s figure,
\nSo the sides of the figure is 2,6,5,2,3,4
\nand the perimeter is 2+6+5+2+3+4= 22 ft.
\nBy this, we can see that the friend’s figure has a greater perimeter,
\nand friend’s perimeter is 22-16= 6 times greater.<\/p>\n
\nDIG DEEPER!<\/strong>
\nExplain how you might use a centimeter ruler and string to estimate the perimeter of the photo of the window.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-16.png\")
\nAnswer:
\nHere, we will use the ruler to find the length of the bottom part of the window and the sides which are straight we can find the length using the ruler. And the curve sides we will measure using the string.<\/p>\n<\/a>Understand Perimeter Homework & Practice 15.1<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-17.png\")
\nThere are ___ units around the figure.
\nSo, the perimeter is ___ inches.
\nAnswer:
\nThere are 20 units around the figure,
\nSo the perimeter is 20 in.<\/p>\n
\nTo find the perimeter of the figure, we will add all the sides of the figure,
\nAs we can see the above image is a square,
\nand the perimeter of the square is s+s+s+s
\n= 5+5+5+5
\n= 20 in.
\nAs there are 20 units around the figure,
\nSo the perimeter is 20 in.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-18.png\")
\nThere are ___ units around the figure.
\nSo, the perimeter is ___ feet.<\/p>\n
\nThere are 32 units around the figure,
\nSo the perimeter is 32 ft.<\/p>\n
\nTo find the perimeter of the figure, we will add all the sides of the figure,
\nThe sides of the above figure is 2,3,4,3,2,5,8,5
\nand the perimeter of the figure is 2+3+4+3+2+5+8+5
\n= 32 units.
\nAs there are 32 units around the figure,
\nSo the perimeter is 32 ft.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-19.png\")
\nPerimeter = ___
\nAnswer:
\nThere are 26 units around the figure,
\nSo the perimeter is 26 cm.<\/p>\n
\nTo find the perimeter of the figure, we will add all the sides of the figure,
\nThe sides of the above figure is 2,2,2,3,1,3,5,8
\nand the perimeter of the figure is 2+2+2+3+1+3+5+8
\n= 26 units.
\nAs there are 26 units around the figure,
\nSo the perimeter is 26 cm.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-20.png\")
\nPerimeter = ___
\nAnswer:
\nThere are 38 units around the figure,
\nSo the perimeter is 38 m.<\/p>\n
\nTo find the perimeter of the figure, we will add all the sides of the figure,
\nThe sides of the above figure is 2,8,2,3,1,3,2,8,2,3,1,3
\nand the perimeter of the figure is 2+8+2+3+1+3+2+8+2+3+1+3
\n= 38 units.
\nAs there are 38 units around the figure,
\nSo the perimeter is 38 m.<\/p>\n
\nDraw a figure that has a perimeter of 18 inches.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-21.png\")
\nAnswer:
\nThe length of the rectangle is 5 in
\nand the breadth of the rectangle is 4 in.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Screenshot-549.png\")
\nLet the length of the rectangle be 5 in
\nand the breadth of the rectangle be 4 in
\nso the perimeter of the rectangle is
\np = 2(length+breadth)
\n= 2(5+4)
\n= 2(9)
\n= 18 in.<\/p>\n
\nReasoning<\/strong>
\nWhich color represents the perimeter of the rectangle? What does the other color represent?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-22.png\")
\nAnswer:
\nBlue color represents the perimeter of the rectangle and
\nthe other color yellow represents the area of the figure.<\/p>\n
\nIn the above figure, the blue color represents the perimeter of the rectangle.
\nBecause the perimeter represents the distance around the edge of the shape.
\nAnd the other color yellow represents the area of the figure,
\nas area represents the amount of space inside a shape.<\/p>\n
\nModeling Real Life
\nUse a centimeter ruler to\ufb01nd the perimeter of the library card.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-24.png\")
\nAnswer:
\nThe perimeter of the library card is 24 cm.<\/p>\n
\nOn measuring, the length of the sides of the library card is 5cm, 7cm, 5cm, 7cm
\nto find the perimeter of the library card, we will add all the length of the sides
\nso the perimeter of the library card is
\np= 5cm+7cm+5cm+7cm
\n= 24 cm
\nThe perimeter of the library card is 24 cm.<\/p>\n
\nModeling Real Life
\nHow much greater is the perimeter of your piece of fabric than the perimeter of your friend\u2019 spiece of fabric?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-25.png\")
\nAnswer:
\nMy fabric is 4 inches greater than my friend’s fabric.<\/p>\n
\nTo find the perimeter of the figure 1, we will add all the sides of the figure,
\nThe sides of the above figure is 2,1,1,2,2,2,8,2,2,2,1,1
\nand the perimeter of the figure is 2+1+1+2+2+2+8+2+2+2+1+1
\n= 26 in.
\nSo the perimeter of the figure is 26 in.
\nAnd now let’s find the perimeter of the friend’s figure,
\nSo the sides of the figure is 1,2,2,4,1,5,4,3
\nand the perimeter is 1+2+2+4+1+5+4+3
\n= 22 in.
\nBy this, we can see that my fabric has the highest perimeter than the friend’s fabric
\nwhich is 26-22= 4 in greater.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-26.png\")
\nAnswer:
\n1= 4\/4 = 6\/6<\/p>\n
\nHere, the equivalent fraction for the whole number means if the numerator was divided by the denominator without any reminder then the fraction is equivalent to a whole number. So 1= 4\/4 = 6\/6.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-27.png\")
\nAnswer:
\n4= 4\/1 = 8\/2.<\/p>\n
\nHere, the equivalent fraction for the whole number means if the numerator was divided by the denominator without any reminder then the fraction is equivalent to a whole number. So 4= 4\/1 = 8\/2.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-28.png\")
\nAnswer:
\n6= 24\/4 = 36\/6.<\/p>\n
\nHere, the equivalent fraction for the whole number means if the numerator was divided by the denominator without any reminder then the fraction is equivalent to a whole number. So 6= 24\/4 = 36\/6.<\/p>\n<\/a>Find Perimeters of Polygons 15.2<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-29.png\")
<\/p>\n
\nThe perimeter of the rectangle is 14 units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-4-2.png\")
\nIn\u00a0 the above figure, we can see the length of the rectangle is 4 units
\nand the breadth of the rectangle is 3 units,
\nso the perimeter of the rectangle is
\np =2(length + breadth)
\n= 2(4+3)
\n= 2(7)
\n= 14 units.
\nThe perimeter of the rectangle is 14 units.
\nCritique the Reasoning of Others<\/strong>
\nCompare your methods of \ufb01nding the perimeter to your partner\u2019s methods. Explain how they are alike or different.
\nAnswer:
\nThere are two methods to find the perimeter explained below.<\/p>\n
\nThere are two ways to find the perimeter.
\nThe first method is
\nPerimeter = 2(length + breadth)
\nhere, we will add length and breadth, and then we will multiply the result by 2.
\nand the second method is
\nPerimeter = a+b+c+d
\nhere, we will add all the sides of the figure.<\/p>\n
\nFind the perimeter of the trapezoid.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-30.png\")
\nYou can find the perimeter of a figure by adding all of the side lengths.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-31.png\")
\nWrite an equation. The letter P represents the unknown perimeter. Add the side lengths.
\nSo, the perimeter is ___.
\nAnswer:
\nSo, the perimeter is 36 in.<\/p>\n
\nTo find the perimeter of the trapezoid, we will add all the sides of the trapezoid,
\nso the sides of the trapezoid is 6 in,12 in,8 in,10 in
\nThe perimeter is 6+12+8+10
\n= 36 in.<\/p>\n
\nFind the perimeter of the rectangle
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-33.png\")
\nBecause a rectangle has two pairs of equal sides, you can also use multiplication to solve.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-34.png\")
\nOne Way:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-35.png\")
\nAnother Way:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-36.png\")
\nSo, the perimeter is ___.<\/p>\n
\nPerimeter = 7+9+7+9
\n= 32 cm.
\nPerimeter=\u00a02\u00d79 + 2\u00d7 7
\n= 32 cm.
\nSo, the perimeter is 32 cm.<\/p>\n
\nTo find the perimeter of a rectangle, we have two ways,
\nOne way is to add all the sides of the rectangle, which is
\n7+9+7+9= 32 cm.
\nAnd the other way is, as the two sides of the rectangle are equal, we wil use formula
\nPerimeter = 2( Length + Breadth)
\n= 2\u00d7 Length + 2 \u00d7 Breadth
\n= 2\u00d79 + 2\u00d7 7
\n= 18+ 14
\n= 32 cm.<\/p>\n
\nAnswer:<\/p>\n
\nTo find the perimeter of the polygon, we will add the length of the all sides.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-37.png\")
\nThe perimeter is ___.
\nAnswer:
\nThe perimeter is 12 m.<\/p>\n
\nTo find the perimeter of the polygon, we will add the length of all sides of the polygon.
\nSo the length of the sides is 5 m, 3 m, 3 m, 2 m
\nThe perimeter is 5+3+3+2
\n= 12 m.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-38.png\")
\nThe perimeter is ___.<\/p>\n
\nThe perimeter is 24 ft.<\/p>\n
\nAs we can see in the above figure which has all sides are equal,
\nso the perimeter of the square is 4s
\n= 4\u00d76
\n= 24 ft.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-39.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the polygon is 28 m.<\/p>\n
\nTo find the perimeter of the polygon, we will add the length of the all sides of the polygon.
\nSo the length of the sides is 4 m, 9 m, 10 m, 5 m
\nThe perimeter is 4+9+10+5
\n= 28 m.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-40.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the figure is 40 in.<\/p>\n
\nTo find the perimeter of the figure, we will add the length of all sides of the figure.
\nSo the length of the sides is 12 in, 4 in, 8 in, 7 in,9 in.
\nThe perimeter is 12+4+8+7+9
\n= 40 in.<\/p>\n
\nRectangle
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-41.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the rectangle is 36 cm.<\/p>\n
\nTo find the perimeter of the rectangle, we need to know the length and the breadth of the rectangle.
\nHere, the length of the rectangle is 9 cm,
\nand the breadth is 10 cm,
\nSo the perimeter of the rectangle is 2(Length + Breadth)
\n= 2(10+9)
\n= 2(19)
\n= 38 cm.<\/p>\n
\nRhombus
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-42.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the Rhombus is 4 in.<\/p>\n
\nAs all sides of the Rhombus are equal, so the formula of the Rhombus is 4a
\nand the side of the Rhombus is 1 in,
\nso the perimeter is 4a
\n= 4\u00d71
\n= 4 in.<\/p>\n
\nParallelogram
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-43.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the parallelogram is 22 cm.<\/p>\n
\nAs the opposite sides of the parallelogram are equal,
\nso the perimeter of the parallelogram is 2(a+b)
\nthe length of the parallelogram is 3 cm,
\nand the breadth of the parallelogram is 8 cm
\nSo the perimeter of the parallelogram is
\n= 2(3+8)
\n= 2(11)
\n= 22 cm.<\/p>\n
\nSquare
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-44.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the square is 16 ft.<\/p>\n
\nAs we can see in the above figure which has all sides are equal,
\nso the perimeter of the square is 4s
\n= 4\u00d74
\n= 16 ft.<\/p>\n
\nYou build a pentagon out of wire for a social studies project. Each side is 8 centimeters long. What is the perimeter of the pentagon?
\nAnswer:
\nThe perimeter of the pentagon is 40 cm.<\/p>\n
\nThe length of the pentagon is 8 cm,
\nso the perimeter of the pentagon is 5a,
\nwhich is 5\u00d78
\n= 40 cm<\/p>\n
\nNumber Sense<\/strong>
\nThe top length of the trapezoid is 4 feet. The bottom length is double the top. The left and right lengths are each 2 feet less than the bottom. Label the side lengths and \ufb01nd the perimeter of the trapezoid.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-45.png\")
\nAnswer:
\nThe sides of the trapezoid are 4ft, 6ft, 8ft, 6ft, and the perimeter is 24 ft.<\/p>\n
\nAs the top length of the trapezoid is 4 feet and the bottom length is double the top,
\nwhich is 4\u00d72= 8 feet. And the left and right lengths are each 2 feet less than the bottom,
\nwhich means 8 – 2 = 6 ft each.<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-2-2.png\")
<\/p>\n
\nThe perimeter of the trapezoid is 4+6+8+6= 24 ft.<\/p>\n
\nWriting<\/strong>
\nExplain how finding the perimeter of a rectangle is different from finding its area.
\nAnswer:
\nPerimeter= 2(length + breadth)
\nArea = length \u00d7 breadth.<\/p>\n
\nTo find the perimeter of the rectangle,
\nwe will add the length and breadth and will multiply the result with 2
\nPerimeter= 2(length + breadth)
\nand to find the area of the rectangle,
\nwe will multiply the length and breadth of the rectangle.
\nArea = length \u00d7 breadth.<\/p>\n
\nDig Deeper!<\/strong>
\nA rectangle has a perimeter of 12 feet. What could its side lengths be ?
\nAnswer:
\nThe length of the rectangle is 4 feet
\nand the breadth of the rectangle is 2 feet<\/p>\n
\nGiven the perimeter is 12 feet,
\nso the let the length be 4 feet
\nand the breadth be 2 feet
\nLet’s check on the length and breadth is correct are not
\nperimeter = 2( length + breadth)
\n= 2( 4+2)
\n= 2(6)
\n= 12 feet.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-46.png\")
\nUnderstand the problem:
\nMake a plan:
\nSolve:
\nThe perimeter is ___.
\nAnswer:
\nThe perimeter of the rectangular sign is 124 ft.<\/p>\n
\nGiven the rectangular sign is 34 feet longer than it’s wide
\nand the wide is 14 ft,
\nso the length is 34ft + 14ft= 48 ft.
\nthe perimeter of the rectangular sign is
\nP= 2(48ft + 14ft)
\n= 2(62ft)
\n= 124 ft.
\nThe perimeter of the rectangular sign is 124 ft.<\/p>\n
\nA city has a rectangular sidewalk in a park. The sidewalk is 4 feet wide and is 96 feet longer than it is wide. What is the perimeter of the sidewalk?
\nAnswer:
\nThe perimeter of the sidewalk is 208 feet.<\/p>\n
\nAs given the rectangular sidewalk’s wide is 4 feet and the length is 96 feet longer than it’s wide,
\nwhich means 96+4= 100 feet is the length of the rectangular sidewalk,
\nso the perimeter of the rectangular sidewalk is 2( length + breadth)
\n= 2( 4+100)
\n= 2(104)
\n= 208 feet.<\/p>\n
\nA team jogs around a rectangular field three times. The field is 80 yards long and 60 yards wide. How many yards does the team jog?
\nAnswer:
\nThe number of yards does the team jog is 3\u00d7280= 840 yards.<\/p>\n
\nThe length of the rectangular field is 80 yards,
\nThe breadth of the rectangular field is 60 yards,
\nSo, the perimeter of the rectangular field is 2(length + breadth)
\n= 2(80+60)
\n= 2(140)
\n= 280 yards.
\nAs the team jogs around a rectangular field three times,
\nso the number of yards does the team jog is 3\u00d7280= 840 yards.<\/p>\n
\nEach side of the tiles is 8 centimeters long. What is the sum of the perimeters?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-47.png\")
\nYou put the tiles together as shown. Is the perimeter of this new shape the same as the sum of the perimeters above? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-48.png\")
\nAnswer:
\nThe sum of the perimeters is 96 cm.
\nYes, there will be a change in the perimeter of the new figure. The perimeter is 80 cm.<\/p>\n
\nIn the above figure, we can see a hexagon that has six sides.
\nSo the formula for the perimeter of a hexagon is 6a,
\nthe perimeter of the tiles is 6\u00d78
\n= 48 cm.
\nSo the sum of the tiles 48+48= 96 cm.
\nYes, there will be a change in the perimeter of the new figure. As there are ten sides in the new figure, so the perimeter of the new figure is 10\u00d78= 80 cm.<\/p>\n<\/a>Find Perimeters of Polygons Homework & Practice 15.2<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-49.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the polygon is 29 in.<\/p>\n
\nThe perimeter of the polygon is the sum of the length of its sides,
\nSo the sides of the polygon are 9 in, 4 in, 6 in, 10 in,
\nand the perimeter of the polygon is 9+4+6+10= 29 in.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-50.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the figure is 38 cm.<\/p>\n
\nThe perimeter of the figure is the sum of the length of its sides,
\nSo the sides of the figure are 6 cm, 5 cm, 7 cm, 8 cm, 7 cm, 5 cm,
\nand the perimeter of the figure is 6+5+7+8+7+5= 38 cm.<\/p>\n
\nSquare
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-51.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the square is 8 ft.<\/p>\n
\nThe length of the square is 2 ft,
\nand the perimeter of the square is 4a
\n= 4\u00d72
\n= 8 ft.
\nso the perimeter of the square is 8 ft.<\/p>\n
\nParallelogram
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-52.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the parallelogram is 8m.<\/p>\n
\nThe length of the parallelogram is 1 m,
\nand the breadth of the parallelogram is 3 m,
\nso the perimeter of the parallelogram is 2(length + breadth)
\n= 2(1+3)
\n= 2(4)
\n= 8 m.<\/p>\n
\nRhombus
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-53.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the rhombus is 40 ft.<\/p>\n
\nThe length of the side of the rhombus is 10 ft,
\nand the perimeter of the rhombus is 4a
\n= 4\u00d710
\n= 40 ft.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-54.png\")
\nPerimeter = ___
\nAnswer:
\nThe perimeter of the rectangle is 22 in.<\/p>\n
\nTo find the perimeter of the rectangle, we need to know the length and the breadth of the rectangle.
\nHere, the length of the rectangle is 7 in,
\nand the breadth is 4 in,
\nSo the perimeter of the rectangle is 2(Length + Breadth)
\n= 2(7+4)
\n= 2(11)
\n= 22 in.<\/p>\n
\nEach side of a triangle is 5 centimeters long. What is the perimeter of the triangle?
\nAnswer:
\nThe perimeter of the triangle is 15 cm.<\/p>\n
\nGiven the length of the side of the triangle is 5 cm,
\nand the perimeter of the triangle is 3a
\n= 3\u00d75
\n= 15 cm.<\/p>\n
\nYou Be The Teacher<\/strong>
\nDescartes says that a square will always have a greater perimeter than a triangle because it has more sides. Is he correct? Explain.
\nAnswer:
\nYes, Descartes is correct.<\/p>\n
\nYes, Descartes is correct. As the square has four sides and the perimeter of the square is 4a.
\nWhereas the triangle has 3 sides and the perimeter of the triangle is 3a.
\nSo the square will always have a greater perimeter than a triangle.<\/p>\n
\nStructure<\/strong>
\nDraw a pentagon and label its sides so that it has the same perimeter as the rectangle.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-55.png\")
\nAnswer:
\nThe length of the side of the pentagon is 4m.<\/p>\n
\nGiven the length of the rectangle is 7 m,
\nand the breadth of the rectangle is 3 m,
\nSo the perimeter of the rectangle is 2( length + breadth)
\n= 2(7+3)
\n= 2(10)
\n= 20 m.
\nHere we have the perimeter of the pentagon which is 20 m,
\nso we should find the sides of the pentagon,
\nAs we know the perimeter of the pentagon is 5a
\n5a= 20
\na= 20\/5
\n= 4 m.
\nSo the length of the side of the pentagon is 4m.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Screenshot-523.png\")
<\/p>\n
\nModeling Real Life<\/strong>
\nAn Olympic swimming pool is 82 feet longer than it is wide. What is the perimeter of the swimming pool?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-150.png\")
\nAnswer:
\nThe perimeter of the swimming pool is 492 ft.<\/p>\n
\nGiven the Olympic swimming pool is 82 feet longer than it’s wide
\nand the wide is 82 ft,
\nso the length of the swimming pool is 82+82= 164 ft
\nthe perimeter of the swimming pool is
\np= 2(length+breadth)
\n= 2(164+82)
\n= 2(246)
\n= 492 ft.
\nThe perimeter of the swimming pool is 492 ft.<\/p>\n
\nModeling Real Life
\nYou put painter\u2019s tape around two rectangular windows. The windows are each 52 inches long and 28 inches wide. How much painter\u2019s tape do you need?
\nAnswer:
\nThe painter’s tape 160 inches.<\/p>\n
\nGiven the length of the window is 52 inches
\nand the width of the window is 28 inches
\nso the perimeter of the window is
\np= 2(length + breadth)
\n= 2(52+28)
\n= 2(80)
\n= 160 inches.
\nSo the painter’s tape 160 inches.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-56.png\")
\nAnswer:
\n737.<\/p>\n
\nOn adding 590+147 we will get 737.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-57.png\")
\nAnswer:
\n894.<\/p>\n
\nOn adding 636+258 we will get 894<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-15-Find-Perimeter-and-Area-58.png\")
\nAnswer:
\n805.<\/p>\n
\nOn adding 476+329 we will get 805<\/p>\n<\/a>Lesson 15.3 Find Unknown Side Lengths<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-59.png\")
<\/p>\n
\nThe fourth side of the map is 4ft.<\/p>\n
\nWe can find the value of the fourth side in two methods
\nFirst method:
\nGiven the perimeter of the map is 20 feet,
\nand the sides of the map is 6 ft, 4 ft, 6ft, X ft.
\nAs we know the perimeter of the rectangle is
\n6+4+6+X= 20 feet
\n16+X= 20
\nX= 20- 16
\n= 4 ft.
\nSecond method:
\nAs we know that the opposite sides of the rectangle are equal, as we know that the length of the side is 4 ft so the other side will also be 4 ft.<\/p>\n
\nHow is finding the unknown side length of a square different from finding the unknown side length of a rectangle?
\nAnswer:
\nRefer below for a detailed explanation.<\/p>\n
\nTo find the unknown side length of the square
\nif we know the perimeter of the square then
\nthe perimeter of the square is
\np= 4a
\nwe will substitute the value of p, on solving we will get the length of the square.
\nand to find the unknown side length of the rectangle,
\nwe need to know the area or perimeter of the rectangle
\nand the other side of the rectangle.
\nso the formula of the perimeter of the rectangle is
\np = 2(length + breadth)
\nwe will substitute the perimeter value and the other side value
\nthen we can find the length of the rectangle.<\/p>\n
\nExample<\/strong>
\nThe perimeter of the trapezoid is 26 feet. Find the unknown side length.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-60.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-61.png\")
\nWrite an equation for the perimeter.
\nAdd the known side lengths.
\nWhat number plus 16 equals 26?
\nThe unknown side length is ___.
\nAnswer:
\nK= 10,
\nThe number 16+10 equals 26.
\nThe unknown side length is 10.<\/p>\n
\nGiven the perimeter of the trapezoid is 26 ft,
\nSo the perimeter of the trapezoid is
\nK+5+6+5= 26
\nK+16= 26
\nK= 10.
\nThe number 16+10 equals 26.
\nThe unknown side length is 10.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-62.png\")
\nThe perimeter of the square is 32 centimeters. Find the length of each side of the square.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-63.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-64.png\")
\nWrite an equation for the perimeter 4 times what number equals 32?
\nSo, the length of each side is ___.
\nAnswer:
\nn= 8.
\nThe length of each side is 8 cm.<\/p>\n
\nThe perimeter of the square is 32 cm
\nSo to find the sides of the square
\n4a= 32
\na= 32\/4
\n= 8 cm.
\nSo, the length of each side is 8 cm.<\/p>\n
\nPerimeter = 34 inches
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-65.png\")
\ny = ___
\nAnswer:
\ny = 13 in.<\/p>\n
\nGiven the perimeter is 34 inches,
\nand the sides of the figure are 10 in, 7 in, 4 in, y in.
\nso the perimeter of the figure is
\n34 in = 10+7+4+y
\n34 = 21+ y
\ny = 34 – 21
\ny = 13.<\/p>\n
\nPerimeter = 20 meters
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-66.png\")
\nj = ___
\nAnswer:
\nThe length of the sides of the square is 5 m.<\/p>\n
\nAs we can see the above figure is a square and the perimeter of the square 20 meters,
\nso the sides of the square are
\nperimeter = 4a
\n20 = 4 j
\nj= 5 m.<\/p>\n
\nPerimeter = 19 feet
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-67.png\")
\ny = ___
\nAnswer:
\nThe perimeter of the figure is 8 ft.<\/p>\n
\nThe perimeter of the figure is 19 feet,
\nand the length of the sides of the figure is 8 ft, 3 ft, y ft.
\nso perimeter = 8 ft + 3 ft + y ft
\n19= 11 ft + y ft
\ny= 19 ft – 11 ft
\n= 8 ft.<\/p>\n
\nPerimeter = 26 centimeters
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-68.png\")
\nd = ___
\nAnswer:
\nd= 4 cm.<\/p>\n
\nThe perimeter of the figure is 26 cm,
\nand the length of the sides of the figure is 10 cm, 5 cm, 7 cm, d cm.
\nso the perimeter of the figure is
\np = 10+5+7+d
\n26 = 22 + d
\nd= 26-22
\n= 4<\/p>\n
\nPerimeter = 30 feet
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-69.png\")
\nk = ___
\nAnswer:
\nk = 11 ft.<\/p>\n
\nGiven the perimeter of the figure is 30 feet,
\nand the length of the sides is 5ft, 12 ft, 2 ft, k ft
\nSo the perimeter of the figure is
\np = 5 + 12 + 2 + k
\n30 ft = 19 ft + k
\nk = 11 ft.<\/p>\n
\nPerimeter = 32 inches
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-70.png\")
\nk = ___
\nAnswer:
\nk= 4 in.<\/p>\n
\nGiven the perimeter of the figure is 32 inches,
\nand the lengths of all sides is 10 in, 4 in, 5 in, 4 in, 5 in, k in.
\nSo the perimeter of the figure is
\np= 10+4+5+4+5+k
\n32 in =\u00a0 28 in + k
\nk= 4 in.<\/p>\n
\nPerimeter = 8 meters
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-71.png\")
\ny = ___
\nAnswer:
\ny = 2 m.<\/p>\n
\nGiven the perimeter of the rhombus is 8 feet,
\nand the length of the side is y m,
\nSo the perimeter of the rhombus is
\np = 4a
\n8 m = 4\u00d7y
\ny = 2 m.<\/p>\n
\nPerimeter = 48 inches
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-72.png\")
\nd = ___
\nAnswer:
\nd = 8 in.<\/p>\n
\nGiven the perimeter of the Hexagon is 48 inches,
\nand the length of the sides is d in
\nSo the perimeter of the hexagon is
\np = 6 a
\n48 in = 6 \u00d7 d in
\nd= 8 in.<\/p>\n
\nNumber Sense<\/strong>
\nA rectangle has a perimeter of 30 centimeters. The left side is 7 centimeters long. What is the length of the top side?
\nAnswer:
\nThe length of the top side is 8 cm.<\/p>\n
\nGiven the perimeter of the rectangle is 30 cm,
\nand the length of the left side of the rectangle is 7 cm,
\nSo let the length of the top side be X,
\nPerimeter of the rectangle is
\nP = 2 (Length + breadth)
\n30 = 2 ( 7 cm + X cm)
\n30 \/ 2 = 7 cm + X cm
\n15 = 7 cm + X cm
\nX = 15 cm – 7 cm
\nX = 8 cm.
\nso, the length of the top side is 8 cm.<\/p>\n
\nWriting<\/strong>
\nA triangle has three equal sides and a perimeter of 21 meters. Explain how to use division to \ufb01nd the side lengths.
\nAnswer:
\nThe length of the side is 7 m.<\/p>\n
\nGiven the perimeter of the triangle is 21 m,
\nand we need to find the side of the lengths,
\nso the perimeter of the triangle is
\np = 3a
\n21 m = 3\u00d7a
\na = 21\/3
\n= 7 m
\nSo the length of the side is 7 m.<\/p>\n
\nDIG DEEPER!<\/strong>
\nNewton draws and labels the square and rectangle below. The perimeter of the combined shape is 36 feet. Find the unknown side length.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-73.png\")
\nAnswer:
\nThe unknown side of the length is 14 ft.<\/p>\n
\nAs the perimeter of the combined shape is 36 feet,
\nand the length of the side of the rectangle is 4 ft, and the other side be X ft
\nand the perimeter of the rectangle is 36 ft,
\nso perimeter = 2 (length + breadth)
\n36 ft\u00a0 = 2( 4 ft + X ft)
\n36\/2 = 4 ft + X ft
\n18 = 4 ft + X ft
\nX= 14 ft.
\nThe unknown side of the length is 14 ft.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-74.png\")
\nUnderstand the problem:
\nMake a plan:
\nSolve:
\nThe lengths of the other three sides are ___, ___, and ___.
\nAnswer:
\nThe lengths of other three sides is 6 m, 9 m, 9 m.<\/p>\n
\nThe perimeter of the rectangular vegetable garden is 30 m
\nas it is in a rectangular shape, so the opposite sides are equal,
\nand the length of the side of the rectangular vegetable garden is 6m,
\nlet the other side be X m
\nso the perimeter is
\np = 2( length + breadth)
\n30 m = 2( 6 m+ X m)
\n30\/2 = 6 + X
\n15 = 6 + X
\nX= 15 – 6
\n= 9 m.
\nSo the lengths of other three sides is 6 m, 9 m, 9 m.<\/p>\n
\nThe perimeter of the rectangular zoo enclosure is 34 meters. What are the lengths of the other three sides?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-75.png\")
\nAnswer:
\nThe lengths of the other three sides are 12 m, 11 m, 11 m.<\/p>\n
\nThe perimeter of the rectangular zoo is 34 m
\nas it is in rectangular shape, so the opposite sides are equal,
\nand the length of the side of the rectangular zoo is 12 m,
\nlet the other side be X m
\nso the perimeter is
\np = 2( length + breadth)
\n34 m = 2( 12 m+ X m)
\n34\/2 = 12 + X
\n17 = 6 + X
\nX= 17 – 6
\n= 11 m.
\nSo the lengths of the other three sides is 12 m, 11 m, 11 m.<\/p>\n
\nThe floor of an apartment is made of two rectangles. The Perimeter is 154 feet. What are the lengths of the other three sides?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-76.png\")
\nAnswer:
\nThe other length of the side of the small rectangle is 7 ft.
\nThe other length of the side of the big rectangle is 30 ft.<\/p>\n
\nGiven the perimeter of the apartment is 154 feet,
\nfirst, we will take the big rectangle,
\nas the opposite sides of the rectangle are equal and the length of the big rectangle is 30 ft
\nso the other length is also 30 ft.
\nas the perimeter of the small rectangle is 38 ft
\nand the length of the one side of the rectangle is 12 ft
\nso the other length of the small rectangle is
\np = 2(length+breadth)
\n38 = 2(12 + breadth)
\n38\/2 = 12+ breadth
\n19= 12 + breadth
\nbreadth= 19 – 12
\n= 7 ft.
\nThe other length of the side is 7 ft.<\/p>\n
\nDIG DEEPER!<\/strong>
\nYou want to make a flower bed in the shape of a pentagon. Two sides of the flower bed are each 7 inches long, and two sides are each 16 inches long. The perimeter is 57 inches. Sketch the flower bed and label all of the side lengths.
\nAnswer:
\nThe length of the other side is 11 ft.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Screenshot-539.png\")
\nGiven the perimeter of the flower bed shaped pentagon is 57 inches
\nand the two sides of the flower bed each is 7 inches long
\nand the other two sides of the flower bed each is 16 inches long
\nthe other side of the flower bed be X
\nthe perimeter of the flower bed is
\np = 7+7+16+16+X
\n57= 46+X
\nX= 11 in.
\nThe length of the other side is 11 ft.<\/p>\n<\/a>Find Unknown Side Lengths Homework & Practice 15.3<\/h3>\n
\nPerimeter = 24 feet
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-77.png\")
\nd = ___
\nAnswer:
\nThe length of the unknown side is 8 ft.<\/p>\n
\nThe perimeter of the triangle is 24 ft,
\nand the lengths of the sides is 10 ft, 6 ft, d ft
\nso the perimeter of the triangle is
\np = 10+6+d
\n24 = 10+6+d
\n24 = 16+d
\nd = 24 – 16
\n=\u00a0 8 ft.
\nThe length of the unknown side is 8 ft.<\/p>\n
\nPerimeter = 46 inches
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-78.png\")
\nk = ___
\nAnswer:
\nThe length of the unknown side is 15 in.<\/p>\n
\nThe perimeter of the figure is 46 inches,
\nand the lengths of the sides is 13 in, 5 in, 13 in, k in
\nso the perimeter of the figure is
\np = 13+5+13+k
\n46 = 31+k
\n46-31 = k
\nk = 15
\n=\u00a0 15 in.
\nThe length of the unknown side is 15 in.<\/p>\n
\nPerimeter = 21 centimeters
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-79.png\")
\ny = ___
\nAnswer:
\nThe length of the unknown side is 7 cm.<\/p>\n
\nThe perimeter of the figure is 21 cm,
\nand the lengths of the sides is 4 cm, 1 cm, 9 cm, y cm
\nso the perimeter of the figure is
\np = 4 cm+ 1 cm+ 9 cm+ y cm
\n21 = 14+ y
\ny = 21 – 14
\ny = 7
\n=\u00a0 7 cm.
\nThe length of the unknown side is 7 cm.<\/p>\n
\nPerimeter = 41 meters
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-80.png\")
\ny = ___
\nAnswer:
\nThe length of the unknown side is 8 m.<\/p>\n
\nThe perimeter of the figure is 41 m,
\nand the lengths of the sides is 3 m, 12 m, 10 m, 8 m, y m
\nso the perimeter of the figure is
\np = 3+12+10+8+y
\n41 = 33 + y
\ny = 41-33
\ny = 8
\n=\u00a0 8 m.
\nThe length of the unknown side is 8 m.<\/p>\n
\nPerimeter = 12 feet
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-81.png\")
\nd = ___
\nAnswer:
\nThe length of the sides of the triangle is 4 ft.<\/p>\n
\nThe perimeter of the triangle is 12 feet,
\nand the length of the side of the triangle is d ft,
\nso the perimeter of the triangle is
\np = 3 a
\n12 = 3 \u00d7 d
\nd = 12\/3
\n= 4 ft.
\nThe length of the sides of the triangle is 4 ft.<\/p>\n
\nPerimeter = 50 inches
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-82.png\")
\nk = ___
\nAnswer:
\nThe length of the sides of the Hexagon is 4 in.<\/p>\n
\nThe perimeter of the Hexagon is 50 inches,
\nand the length of the side of the Hexagon is k in,
\nso the perimeter of the hexagon is
\np = 5 a
\n50 = 5 \u00d7 k
\nk = 50\/5
\n= 10 in.
\nThe length of the sides of the triangle is 10 in.<\/p>\n
\nDIG DEEPER!<\/strong>
\nEach polygon has equal side lengths that are whole numbers. Which polygon could have a perimeter of 16 centimeters? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-83.png\")
\nAnswer:
\nThe length of the sides of the octagon is 2 cm.<\/p>\n
\nIn the above three polygons, the second figure is an octagon, which has eight sides.
\nand the perimeter of the octagon is
\np = 8 a
\n16 cm = 8 a
\na = 16 \/8
\n= 2 cm.<\/p>\n
\nNumber Sense<\/strong>
\nThe area of a square is 25 square inches. What is its perimeter?
\nAnswer:
\nThe perimeter of the square is 20 inches.<\/p>\n
\nThe area of the square is 25 square inches, so
\narea = s^2
\n25 = s^2
\ns= 5 inches
\nso the perimeter of the square is
\np = 4s
\n= 4\u00d75
\n= 20 inches.<\/p>\n
\nModeling Real Life<\/strong>
\nThe perimeter of the rectangular side walk is 260 meters. What are the lengths of the other three sides?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-84.png\")
\nAnswer:
\nThe length of the other three sides is 10 m,10m,120 m.<\/p>\n
\nThe perimeter of the rectangular side walk is 260 meters,
\nand the length of the one side of the side walk is 120 m,
\nso the perimeter of the rectangular side walk is
\np = 2( length + breadth)
\n260 = 2 ( 120 + breadth)
\n260\/2 = 120 + breadth
\n130 = 120 + breadth
\nbreadth = 130 – 120
\n= 10 m.
\nThe length of the other three sides is 10 m,10m,120 m.<\/p>\n
\nModeling Real Life<\/strong>
\nTwo rectangular tables are pushed together. The perimeter is 40 feet. What are the lengths of the other three sides?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-85.png\")
\nAnswer:
\nThe other length of the side of the small rectangle is 3 ft.
\nThe other length of the side of the big rectangle is 5 ft.<\/p>\n
\nGiven the perimeter of the apartment is 40 feet,
\nfirst, we will take the big rectangle,
\nas the opposite sides of the rectangle are equal
\nand the length of the big rectangle is 5 ft
\nso the other length is also 5 ft.
\nas the perimeter of the small rectangle is 10 ft
\nand the length of the one side of the rectangle is 2 ft
\nso the other length of the small rectangle is
\np = 2(length+breadth)
\n10 = 2(2 + breadth)
\n10\/2 = 2+ breadth
\n5= 2 + breadth
\nbreadth= 5 – 2
\n= 3 ft.
\nThe other length of the side is 3 ft.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-86.png\")
\nAnswer:
\n06: 48<\/p>\n
\nAnother way to say time is 06: 48<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-87.png\")
\nAnswer:
\n03: 24<\/p>\n
\nAnother way to say time is 03: 24<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-88.png\")
\nAnswer:<\/p>\n
\nAnother way to say the time is 11: 48<\/p>\n<\/a>Lesson 15.4 Same Perimeter, Different Areas<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-89.png\")
<\/p>\n
\nNo, the area of rectangle 1 and rectangle 2 is not the same.<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-4-3.png\")
\nGiven the perimeter of the rectangle is 16 units
\nThe length of rectangle 1 is 5 units
\nand the breadth of rectangle 1 is 3 units
\nso the area of rectangle 1 is
\narea = length \u00d7 breadth
\n= 5\u00d73
\n= 15 square units.
\nThe length of rectangle 2 is 6 units
\nand the breadth of rectangle 2 is 2 units
\nso the area of rectangle 2 is
\narea = length \u00d7 breadth
\n= 6\u00d72
\n= 12 square units.
\nNo, the area of rectangle 1 and rectangle 2 is not the same.<\/p>\n
\nDraw another rectangle that has the same perimeter but different dimensions. Compare the area of the new rectangle to the rectangles above. What do you notice?
\nAnswer:
\nNo, the area of rectangle 1 and rectangle 2 is not the same.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-4-4.png\")
\nThe length of rectangle 1 is 4 units
\nand the breadth of rectangle 1 is 3 units
\nthe perimeter of rectangle 1 is
\np= 2(length+breadth)
\n= 2(4+3)
\n= 2(7)
\n= 14 units.
\nso the area of rectangle 1 is
\narea = length \u00d7 breadth
\n= 4\u00d73
\n= 12 square units.
\nThe length of rectangle 2 is 5 units
\nand the breadth of rectangle 2 is 2 units
\nthe perimeter of rectangle 1 is
\np= 2(length+breadth)
\n= 2(5+2)
\n= 2(7)
\n= 14 units.
\nso the area of rectangle 2 is
\narea = length \u00d7 breadth
\n= 5\u00d72
\n= 10 square units.
\nNo, the area of rectangle 1 and rectangle 2 is not the same.<\/p>\n
\nFind the perimeter and the area of Rectangle A. Draw a different rectangle that has the same perimeter. Which rectangle has the greater area?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-90.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-91.png\")
\nRectangle ___ has a greater area.
\nAnswer:
\nThe perimeter of the rectangle A is 20 m
\nand the area of the rectangle A is 24 m2<\/sup>
\nThe perimeter of rectangle B is 20 m
\nand the area of the rectangle B is 16 m2<\/sup>
\nThe rectangle A has a greater area.<\/p>\n
\nGiven the length of the rectangle is 6m
\nand the breadth of the rectangle is 4m,
\nso the perimeter of the rectangle is
\np = 2( length + breadth)
\n= 2(6 + 4)
\n= 2(10)
\n= 20 m.
\nAnd the area of the rectangle is
\na = length \u00d7 breadth
\n= 6 \u00d7 4
\n= 24 m2<\/sup><\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-3-2.png\")
<\/p>\n
\nand the breadth is 2m,
\nso the perimeter of the rectangle is
\np = 2(length + breadth)
\n= 2(8 + 2)
\n= 2(10)
\n= 20 m.
\nAnd the area of the rectangle is
\narea = length \u00d7 breadth
\n= 8\u00d72
\n= 16 m2<\/sup>
\nSo the rectangle A has a greater area.<\/p>\n
\nFind the perimeter and area of Rectangle A. Draw a different rectangle that has the same perimeter. Which rectangle has the greater area?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-92.png\")
\nPerimeter = ___
\nArea = ___
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-93.png\")
\nPerimeter = ___
\nArea = ___
\nRectangle ___ has the greater area.
\nAnswer:The perimeter of the rectangle A is 14 in
\nand the area of the rectangle A is 10 in2<\/sup>
\nThe perimeter of rectangle B is 14 in
\nand the area of the rectangle B is 12 in2<\/sup>
\nThe rectangle B has a greater area.<\/p>\n
\nGiven the length of the rectangle is 5 in
\nand the breadth of the rectangle is 2 in,
\nso the perimeter of the rectangle is
\np = 2( length + breadth)
\n= 2(5 + 2)
\n= 2(7)
\n= 14 in.
\nAnd the area of the rectangle is
\na = length \u00d7 breadth
\n= 5\u00d72
\n= 10 in2<\/sup><\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-3-3.png\")
<\/p>\n
\nand the breadth is 3 in,
\nso the perimeter of the rectangle is
\np = 2(length + breadth)
\n= 2(4 + 3)
\n= 2(7)
\n= 14 in.
\nAnd the area of the rectangle is
\narea = length \u00d7 breadth
\n= 4\u00d73
\n= 12 in2<\/sup>
\nSo the rectangle B has a greater area.<\/p>\n
\nRectangle A
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-94.png\")
\nPerimeter = ___
\nArea = ___
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-95.png\")
\nPerimeter = ___
\nArea = ___
\nRectangle ___ has the greater area.
\nAnswer:
\nThe perimeter of the rectangle A is 22 cm
\nand the area of the rectangle A is 11 cm2<\/sup>
\nThe perimeter of rectangle B is 22 cm
\nand the area of the rectangle B is 30 cm2<\/sup>
\nThe rectangle B has a greater area.<\/p>\n
\nGiven the length of the rectangle is 10 cm,
\nand the breadth of the rectangle is 1 cm,
\nso the perimeter of the rectangle is
\np = 2( length + breadth)
\n= 2(10 + 1)
\n= 2(11)
\n= 22 cm.
\nAnd the area of the rectangle is
\na = length \u00d7 breadth
\n= 11 \u00d7 1
\n= 11 cm2<\/sup><\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-3.png\")
<\/p>\n
\nand the breadth is 5 cm,
\nso the perimeter of the rectangle is
\np = 2(length + breadth)
\n= 2(6 + 5)
\n= 2(11)
\n= 22 cm.
\nAnd the area of the rectangle is
\narea = length \u00d7 breadth
\n= 6\u00d75
\n= 30 cm2<\/sup>
\nSo the rectangle B has a greater area.<\/p>\n
\nRectangle A
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-96.png\")
\nPerimeter = ___
\nArea = ___<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-97.png\")
\nPerimeter = ___
\nArea = ___
\nRectangle ___ has the greater area
\nAnswer:
\nThe perimeter of the rectangle A is 20 m
\nand the area of the rectangle A is 21 m2<\/sup>
\nThe perimeter of rectangle B is 20 m
\nand the area of the rectangle B is 24 m2<\/sup>
\nThe rectangle B has a greater area.<\/p>\n
\nGiven the length of the rectangle is 7 m,
\nand the breadth of the rectangle is 3 m,
\nso the perimeter of the rectangle is
\np = 2( length + breadth)
\n= 2(7 + 3)
\n= 2(10)
\n= 20 m.
\nAnd the area of the rectangle is
\na = length \u00d7 breadth
\n= 7 \u00d7 3
\n= 21 m2<\/sup><\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-3-1.png\")
<\/p>\n
\nand the breadth is 4 m,
\nso the perimeter of the rectangle is
\np = 2(length + breadth)
\n= 2(6 + 4)
\n= 2(10)
\n= 20 m.
\nAnd the area of the rectangle is
\narea = length \u00d7 breadth
\n= 6\u00d74
\n= 24 m2<\/sup>
\nSo the rectangle B has a greater area.<\/p>\n
\nMP Structure
\nDraw a rectangle that has the same perimeter as the one shown, but with a lesser area. What is the area ?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-98.png\")
<\/p>\n
\nThe perimeter of the rectangle A is 26 ft
\nand the area of the rectangle A is 40 ft2<\/sup>
\nThe perimeter of rectangle B is 26 ft
\nand the area of the rectangle B is 30 ft2<\/sup>
\nThe rectangle B has a greater area.<\/p>\n
\nGiven the length of the rectangle is 5 ft,
\nand the breadth of the rectangle is 8 ft,
\nso the perimeter of the rectangle is
\np = 2( length + breadth)
\n= 2(5 + 8)
\n= 2(13)
\n= 26 ft.
\nAnd the area of the rectangle is
\na = length \u00d7 breadth
\n= 5 \u00d7 8
\n= 40 ft<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/screenshot-3-4.png\")
<\/p>\n
\nand the breadth is 3 ft,
\nso the perimeter of the rectangle is
\np = 2(length + breadth)
\n= 2(10 + 3)
\n= 2(13)
\n= 26 ft.
\nAnd the area of the rectangle is
\narea = length \u00d7 breadth
\n= 10\u00d73
\n= 30 ft2<\/sup>
\nSo the rectangle A has a greater area.<\/p>\n
\nDraw to show:
\nShe should make the roped-off section ___ meters long and ___ meters wide.
\nAnswer:
\nShe should make the roped-off section 4 meters long and 2 meters wide.<\/p>\n
\nGiven that a paleontologist has 12 meters of twine to rope off a rectangular section,
\nso if we take the length as 4 m and width as 2 m then we can get the greatest possible area,
\nso the area of the rectangular section is
\narea = length \u00d7 breadth
\n= 4 m \u00d72 m
\n= 8 m2<\/sup><\/p>\n
\nNewton has 16 feet of wood to make a rectangular sandbox. How long and wide should he make the sandbox so it has the greatest possible area?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-99.png\")
\nAnswer:
\nThe greatest possible area of the rectangular sandbox is 15 ft2<\/sup><\/p>\n
\nAs Newton has 16 feet of wood to make a rectangular sandbox,
\nso let the length be 5 ft and the wide be 3 ft to get the greatest possible area,
\nso the area of the rectangular sandbox is
\narea = length \u00d7 breadth
\n= 5 ft \u00d7 3 ft
\n= 15 ft2<\/sup>
\nThe greatest possible area of the rectangular sandbox is 15 ft2<\/sup><\/p>\n
\nDIG DEEPER!<\/strong>
\nYou and Newton are building forts. You each have the same length of rope to make a rectangular perimeter for the forton the ground. Your roped-off section is shown. Newton\u2019s section has a greater area than yours. Draw one way Newton could rope off his fort.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-15-Find-Perimeter-and-Area-100.png\")
<\/p>\n
\nRefer the below for detailed explanation.<\/p>\n
\nThe length of the rope is 7 ft
\nand the breadth of the rope is 3 ft
\nthe perimeter is
\np = 2(length+breadth)
\n= 2(7+3)
\n= 2(10)
\n= 20 ft.
\nThe area of the rectangle is
\narea= length\u00d7breadth
\n= 7\u00d73
\n= 21 square feet.<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Screenshot-541.png\")
\nLet the length of the Newton’s rope is 6 ft
\nand the breadth of the Newton’s rope is 4 ft
\nthe perimeter is
\np = 2(length+breadth)
\n= 2(6+4)
\n= 2(10)
\n= 20 ft.
\nThe area of the rectangle is
\narea= length\u00d7breadth
\n= 6\u00d74
\n= 24 square feet.
\nAnd here Newton’s area is greater.<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Screenshot-543.png\")
<\/p>\n
\nand the breadth of the Descarte’s rope is 2 ft
\nthe perimeter is
\np = 2(length+breadth)
\n= 2(8+2)
\n= 2(10)
\n= 20 ft.
\nThe area of the rectangle is
\narea= length\u00d7breadth
\n= 8\u00d72
\n= 16 square feet.
\nAnd here Descartes area is lesser.<\/p>\n<\/a>Same Perimeter, Different Areas Homework & Practice 15.4<\/h3>\n
\nFind the perimeter and the area of Rectangle A. Draw a different rectangle that has the same perimeter? Which rectangle has the greater area?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-101.png\")
\nPerimeter = ___
\nArea = ___
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-102.png\")
\nPerimeter = ___
\nArea = ___
\nRectangle __ has the greater area.
\nAnswer:
\nThe perimeter of the rectangle A is 7 cm
\nand the area of the rectangle A is 24 cm2<\/sup>
\nThe perimeter of rectangle B is 26 ft
\nand the area of the rectangle B is 30 ft2
\nThe rectangle B has a greater area.<\/p>\n
\nGiven the length of the rectangle is 7 cm,
\nand the breadth of the rectangle is 5 cm,
\nso the perimeter of the rectangle is
\np = 2( length + breadth)
\n= 2(7 + 5)
\n= 2(12)
\n= 24 cm.
\nAnd the area of the rectangle is
\na = length \u00d7 breadth
\n= 7 \u00d7 5
\n= 35 cm2<\/sup>.<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Screenshot-545.png\")
<\/p>\n
\nand the breadth is 5.5 cm,
\nso the perimeter of the rectangle is
\np = 2(length + breadth)
\n= 2(6.5 + 5.5)
\n= 2(12)
\n= 24 ft.
\nAnd the area of the rectangle is
\narea = length \u00d7 breadth
\n= 6.5\u00d75.5
\n= 35.75 square feet
\nSo the rectangle B has a greater area.<\/p>\n
\nPatterns<\/strong>
\nComplete the pattern. Find the area of each rectangle.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-103.png\")
\nEach rectangle has the same perimeter. As the area increases, what do you notice about the shape of the rectangle?
\nAnswer:
\nAs the area increases the shape of the figure was changed, we can see the figure was changed from rectangle to square.<\/p>\n
\nAs we know that the perimeter of the above figure is the same,
\nso the perimeter of the above figures is
\np = 2 (length + breadth)
\n= 2 (1 m+9 m)
\n= 2(10 m)
\n= 20 m.
\nSo, the perimeter of the above figures is 20 m.
\nThe area of figure 1 is
\narea = length \u00d7 breadth
\n= 1 m \u00d7 9 m
\n= 9 m2<\/sup>.
\nThe area of figure 2 is
\n= 8m \u00d7 2m
\n= 16 m2<\/sup>.
\nThe area of figure 3 is
\n= 7m \u00d7 3m
\n= 21 m2<\/sup>.
\nLet the length of figure 4 be 6m and the breadth be 4m,
\nThe area of figure 4 is
\n= 6m \u00d7 4m
\n= 24 m2<\/sup>.
\nLet the length of figure 5 be 5m and the breadth be 5m,
\nThe area of figure 5 is
\n= 5m \u00d7 5m
\n= 25 m2<\/sup>.<\/p>\n
\nModeling Real Life<\/strong>
\nYou are making a card with a 36-centimeter ribbon border. How long and wide should you make the card so you have the greatest possible area to write?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-104.png\")
\nAnswer:
\nThe length and the breadth of the card is 9 cm.<\/p>\n
\nGiven the perimeter of the card with a ribbon border is 36 cm
\nso the length of the card is
\np =4a
\n36 = 4a
\na= 36\/4
\n= 9 cm.
\nThe length and the breadth of the card is 9 cm.
\nThe area of the card is
\na = length\u00d7breadth
\n= 9\u00d79
\n= 81 square cm.<\/p>\n
\nDIG DEEPER!<\/strong>
\nA school has two rectangular playgrounds that each have the same perimeter. The first playground is shown. The second has a lesser area than the first. Draw one way the second playground could look.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-15-Find-Perimeter-and-Area-105.png\")
<\/p>\n
\nAnswer:<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Screenshot-547.png\")
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