# Exercises: Use Properties of Rectangles, Triangles, and Trapezoids (6.2)

**Exercises: Understand Linear, Square, and Cubic Measure**

Instructions: For questions 1-6, determine whether you would measure each item using linear, square, or cubic units.

**1. amount of water in a fish tank**

**Solution**

cubic

**2. length of dental floss**

**3. living area of an apartment**

**Solution**

square

**4. floor space of a bathroom tile**

**5. height of a doorway**

**Solution**

linear

**6. capacity of a truck trailer**

**Exercises: Find the Perimeter**

Instructions: For questions 7-12, find each figure’s:

a. perimeter

b. area

Assume each side of the square is [latex]1[/latex] cm.

**7.**

**Solution**

a. [latex]10[/latex] cm

b. [latex]4[/latex] sq. cm

**8.**

**9.**

**Solution**

a. [latex]8[/latex] cm

b. [latex]3[/latex] sq. cm

**10.**

**11.**

**Solution**

a. [latex]10[/latex] cm

b. [latex]5[/latex] sq. cm

**12.**

**Exercises: Use the Properties of Rectangles**

Instructions: For each rectangle in questions 13-16, find the:

a. perimeter

b. area

**13. The length of a rectangle is [latex]85[/latex] feet and the width is [latex]45[/latex] feet.**

**Solution**

a. [latex]260[/latex] ft

b. [latex]3825[/latex] sq. ft

**14. The length of a rectangle is [latex]26[/latex] inches and the width is [latex]58[/latex] inches.**

**15. A rectangular room is [latex]15[/latex] feet wide by [latex]14[/latex] feet long.**

**Solution**

a. [latex]58[/latex] ft

b. [latex]210[/latex] sq. ft

**16. A driveway is in the shape of a rectangle [latex]20[/latex] feet wide by [latex]35[/latex] feet long.**

**Exercises: ****Use the Properties of Rectangles**

**17. Find the length of a rectangle with perimeter [latex]124[/latex] inches and width [latex]38[/latex] inches.**

**Solution**

[latex]24[/latex] inches

**18. Find the length of a rectangle with perimeter [latex]20.2[/latex] yards and width of [latex]7.8[/latex] yards.**

**19. Find the width of a rectangle with perimeter [latex]92[/latex] meters and length [latex]19[/latex] meters.**

**Solution**

[latex]27[/latex] meters

**20. Find the width of a rectangle with perimeter [latex]16.2[/latex] meters and length [latex]3.2[/latex] meters.**

**21. The area of a rectangle is [latex]414[/latex] square meters. The length is [latex]18[/latex] meters. What is the width?**

**Solution**

[latex]23[/latex] m

**22. The area of a rectangle is [latex]782[/latex] square centimeters. The width is [latex]17[/latex] centimeters. What is the length?**

**23. The length of a rectangle is [latex]9[/latex] inches more than the width. The perimeter is [latex]46[/latex] inches. Find the length and the width.**

**Solution**

[latex]7[/latex] in., [latex]16[/latex] in.

**24. The width of a rectangle is [latex]8[/latex] inches more than the length. The perimeter is [latex]52[/latex] inches. Find the length and the width.**

**25. The perimeter of a rectangle is [latex]58[/latex] meters. The width of the rectangle is [latex]5[/latex] meters less than the length. Find the length and the width of the rectangle.**

**Solution**

[latex]17[/latex] m, [latex]12[/latex] m

**26. The perimeter of a rectangle is [latex]62[/latex] feet. The width is [latex]7[/latex] feet less than the length. Find the length and the width.**

**27. The width of the rectangle is [latex]0.7[/latex] meters less than the length. The perimeter of a rectangle is [latex]52.6[/latex] meters. Find the dimensions of the rectangle.**

**Solution**

[latex]13.5[/latex] m, [latex]12.8[/latex] m

**28. The length of the rectangle is [latex]1.1[/latex] meters less than the width. The perimeter of a rectangle is [latex]49.4[/latex] meters. Find the dimensions of the rectangle.**

**29. The perimeter of a rectangle of [latex]150[/latex] feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.**

**Solution**

[latex]25[/latex] ft, [latex]50[/latex] ft

**30. The length of a rectangle is three times the width. The perimeter is [latex]72[/latex] feet. Find the length and width of the rectangle.**

**31. The length of a rectangle is [latex]3[/latex] meters less than twice the width. The perimeter is [latex]36[/latex] meters. Find the length and width.**

**Solution**

[latex]7[/latex] m, [latex]11[/latex] m

**32. The length of a rectangle is [latex]5[/latex] inches more than twice the width. The perimeter is [latex]34[/latex] inches. Find the length and width.**

**33. The width of a rectangular window is [latex]24[/latex] inches. The area is [latex]624[/latex] square inches. What is the length?**

**Solution**

[latex]26[/latex] in.

**34. The length of a rectangular poster is [latex]28[/latex] inches. The area is [latex]1316[/latex] square inches. What is the width?**

**35. The area of a rectangular roof is [latex]2310[/latex] square meters. The length is [latex]42[/latex] meters. What is the width?**

**Solution**

[latex]55[/latex] m

**36. The area of a rectangular tarp is [latex]132[/latex] square feet. The width is [latex]12[/latex] feet. What is the length?**

**37. The perimeter of a rectangular courtyard is [latex]160[/latex] feet. The length is [latex]10[/latex] feet more than the width. Find the length and the width.**

**Solution**

[latex]35[/latex] ft, [latex]45[/latex] ft

**38. The perimeter of a rectangular painting is [latex]306[/latex] centimeters. The length is [latex]17[/latex] centimeters more than the width. Find the length and the width.**

**39. The width of a rectangular window is [latex]40[/latex] inches less than the height. The perimeter of the doorway is [latex]224[/latex] inches. Find the length and the width.**

**Solution**

[latex]76[/latex] in., [latex]36[/latex] in.

**40. The width of a rectangular playground is [latex]7[/latex] meters less than the length. The perimeter of the playground is [latex]46[/latex] meters. Find the length and the width.**

**Exercises: Use the Properties of Triangles**

Instructions: For questions 41-68, solve using the properties of triangles.

**41. Find the area of a triangle with base [latex]12[/latex] inches and height [latex]5[/latex] inches.**

**Solution**

[latex]30[/latex] sq. in.

**42. Find the area of a triangle with base [latex]45[/latex] centimeters and height [latex]30[/latex] centimeters.**

**43. Find the area of a triangle with base [latex]8.3[/latex] meters and height [latex]6.1[/latex] meters.**

**Solution**

[latex]25.315[/latex] sq. m

**44. Find the area of a triangle with base [latex]24.2[/latex] feet and height [latex]20.5[/latex] feet.**

**45. A triangular flag has base of [latex]1[/latex] foot and height of [latex]1.5[/latex] feet. What is its area?**

**Solution**

[latex]0.75[/latex] sq. ft

**46. A triangular window has base of [latex]8[/latex] feet and height of [latex]6[/latex] feet. What is its area?**

**47. If a triangle has sides of [latex]6[/latex] feet and [latex]9[/latex] feet and the perimeter is [latex]23[/latex] feet, how long is the third side?**

**Solution**

[latex]8[/latex] ft

**48. If a triangle has sides of [latex]14[/latex] centimeters and [latex]18[/latex] centimeters and the perimeter is [latex]49[/latex] centimeters, how long is the third side?**

**49. What is the base of a triangle with an area of [latex]207[/latex] square inches and height of [latex]18[/latex] inches?**

**Solution**

[latex]23[/latex] in.

**50. What is the height of a triangle with an area of [latex]893[/latex] square inches and base of [latex]38[/latex] inches?**

**51. The perimeter of a triangular reflecting pool is [latex]36[/latex] yards. The lengths of two sides are [latex]10[/latex] yards and [latex]15[/latex] yards. How long is the third side?**

**Solution**

[latex]11[/latex] ft

**52. A triangular courtyard has perimeter of [latex]120[/latex] meters. The lengths of two sides are [latex]30[/latex] meters and [latex]50[/latex] meters. How long is the third side?**

**53. An isosceles triangle has a base of [latex]20[/latex] centimeters. If the perimeter is [latex]76[/latex] centimeters, find the length of each of the other sides.**

**Solution**

[latex]28[/latex] cm

**54. An isosceles triangle has a base of [latex]25[/latex] inches. If the perimeter is [latex]95[/latex] inches, find the length of each of the other sides.**

**55. Find the length of each side of an equilateral triangle with a perimeter of [latex]51[/latex] yards.**

**Solution**

[latex]17[/latex] ft

**56. Find the length of each side of an equilateral triangle with a perimeter of [latex]54[/latex] meters.**

**57. The perimeter of an equilateral triangle is [latex]18[/latex] meters. Find the length of each side.**

**Solution**

[latex]6[/latex] m

**58. The perimeter of an equilateral triangle is [latex]42[/latex] miles. Find the length of each side.**

**59. The perimeter of an isosceles triangle is [latex]42[/latex] feet. The length of the shortest side is [latex]12[/latex] feet. Find the length of the other two sides.**

**Solution**

[latex]15[/latex] ft

**60. The perimeter of an isosceles triangle is [latex]83[/latex] inches. The length of the shortest side is [latex]24[/latex] inches. Find the length of the other two sides.**

**61. A dish is in the shape of an equilateral triangle. Each side is [latex]8[/latex] inches long. Find the perimeter.**

**Solution**

[latex]24[/latex] in.

**62. A floor tile is in the shape of an equilateral triangle. Each side is [latex]1.5[/latex] feet long. Find the perimeter.**

**63. A road sign in the shape of an isosceles triangle has a base of [latex]36[/latex] inches. If the perimeter is [latex]91[/latex] inches, find the length of each of the other sides.**

**Solution**

[latex]27.5[/latex] in.

**64. A scarf in the shape of an isosceles triangle has a base of [latex]0.75[/latex] meters. If the perimeter is [latex]2[/latex] meters, find the length of each of the other sides.**

**65. The perimeter of a triangle is [latex]39[/latex] feet. One side of the triangle is [latex]1[/latex] foot longer than the second side. The third side is [latex]2[/latex] feet longer than the second side. Find the length of each side.**

**Solution**

[latex]12[/latex] ft, [latex]13[/latex] ft, [latex]14[/latex] ft

**66. The perimeter of a triangle is [latex]35[/latex] feet. One side of the triangle is [latex]5[/latex] feet longer than the second side. The third side is [latex]3[/latex] feet longer than the second side. Find the length of each side.**

**67. One side of a triangle is twice the smallest side. The third side is [latex]5[/latex] feet more than the shortest side. The perimeter is [latex]17[/latex] feet. Find the lengths of all three sides.**

**Solution**

[latex]3[/latex] ft, [latex]6[/latex] ft, [latex]8[/latex] ft

**68. One side of a triangle is three times the smallest side. The third side is [latex]3[/latex] feet more than the shortest side. The perimeter is [latex]13[/latex] feet. Find the lengths of all three sides.**

**Exercises: Use the Properties of Trapezoids**

**69. The height of a trapezoid is [latex]12[/latex] feet and the bases are [latex]9[/latex] and [latex]15[/latex] feet. What is the area?**

**Solution**

[latex]144[/latex] sq. ft

**70. The height of a trapezoid is [latex]24[/latex] yards and the bases are [latex]18[/latex] and [latex]30[/latex] yards. What is the area?**

**71. Find the area of a trapezoid with a height of [latex]51[/latex] meters and bases of [latex]43[/latex] and [latex]67[/latex] meters.**

**Solution**

[latex]2805[/latex] sq. m

**72. Find the area of a trapezoid with a height of [latex]62[/latex] inches and bases of [latex]58[/latex] and [latex]75[/latex] inches.**

**73. The height of a trapezoid is [latex]15[/latex] centimeters and the bases are [latex]12.5[/latex] and [latex]18.3[/latex] centimeters. What is the area?**

**Solution**

[latex]231[/latex] sq. cm

**74. The height of a trapezoid is [latex]48[/latex] feet and the bases are [latex]38.6[/latex] and [latex]60.2[/latex] feet. What is the area?**

**75. Find the area of a trapezoid with a height of [latex]4.2[/latex] meters and bases of [latex]8.1[/latex] and [latex]5.5[/latex] meters.**

**Solution**

[latex]28.56[/latex] sq. m

**76. Find the area of a trapezoid with a height of [latex]32.5[/latex] centimeters and bases of [latex]54.6[/latex] and [latex]41.4[/latex] centimeters.**

**77. Laurel is making a banner shaped like a trapezoid. The height of the banner is [latex]3[/latex] feet and the bases are [latex]4[/latex] and [latex]5[/latex] feet. What is the area of the banner?**

**Solution**

[latex]13.5[/latex] sq. ft

**78. Niko wants to tile the floor of his bathroom. The floor is shaped like a trapezoid with width [latex]5[/latex] feet and lengths [latex]5[/latex] feet and [latex]8[/latex] feet. What is the area of the floor?**

**79. Theresa needs a new top for her kitchen counter. The counter is shaped like a trapezoid with width [latex]18.5[/latex] inches and lengths [latex]62[/latex] and [latex]50[/latex] inches. What is the area of the counter?**

**Solution**

[latex]1036[/latex] sq. in.

**80. Elena is knitting a scarf. The scarf will be shaped like a trapezoid with width [latex]8[/latex] inches and lengths [latex]48.2[/latex] inches and [latex]56.2[/latex] inches. What is the area of the scarf?**

**Exercises: Everyday Math**

**81. Fence.**Jose just removed the children’s playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a [latex]50[/latex] foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be [latex]10[/latex] feet. How long can he make the other side if he wants to use the entire roll of fence?**Solution**

[latex]15[/latex] ft

**82. Gardening.**Lupita wants to fence in her tomato garden. The garden is rectangular and the length is twice the width. It will take [latex]48[/latex] feet of fencing to enclose the garden. Find the length and width of her garden.

**83. Fence.**Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are [latex]6[/latex] feet, [latex]8[/latex] feet, and [latex]10[/latex] feet. The fence costs [latex]$10[/latex] per foot. How much will it cost for Christa to fence in her flowerbed?**Solution**

[latex]$24[/latex]

**84. Painting.**Caleb wants to paint one wall of his attic. The wall is shaped like a trapezoid with height [latex]8[/latex] feet and bases [latex]20[/latex] feet and [latex]12[/latex] feet. The cost of the painting one square foot of wall is about [latex]$0.05.[/latex] About how much will it cost for Caleb to paint the attic wall?**Exercises: Writing Exercises**

**85. If you need to put tile on your kitchen floor, do you need to know the perimeter or the area of the kitchen? Explain your reasoning.**

**Solution**

Answers will vary.

**86. If you need to put a fence around your backyard, do you need to know the perimeter or the area of the backyard? Explain your reasoning.**

**87. Look at the two figures.**

**a. Which figure looks like it has the larger area? Which looks like it has the larger perimeter?**

**b. Now calculate the area and perimeter of each figure. Which has the larger area? Which has the larger perimeter?**

**Solution**

Answers will vary.

**87. The length of a rectangle is [latex]5[/latex] feet more than the width. The area is [latex]50[/latex] square feet. Find the length and the width.**

**a. Write the equation you would use to solve the problem.**

**b. Why can’t you solve this equation with the methods you learned in the previous chapter?**