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.

A rectangle is shown comprised of 4 squares forming a horizontal line.
Figure 6P.2.1
Solution

a. [latex]10[/latex] cm
b. [latex]4[/latex] sq. cm

8.

A rectangle is shown comprised of 3 squares forming a vertical line.
Figure 6P.2.2

9.

Three squares are shown. There is one on the bottom left, one on the bottom right, and one on the top right.
Figure 6P.2.3
Solution

a. [latex]8[/latex] cm
b. [latex]3[/latex] sq. cm

10.

Four squares are shown. Three form a horizontal line, and there is one above the center square.
Figure 6P.2.4

11.

Five squares are shown. There are three forming a horizontal line across the top and two underneath the two on the right.
Figure 6P.2.5
Solution

a. [latex]10[/latex] cm
b. [latex]5[/latex] sq. cm

12.

A square is shown. It is comprised of nine smaller squares.
Figure 6P.2.6

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

Instructions: For questions 17-40, solve.
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

Instructions: For questions 69-80, solve using 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

Instructions: For questions 81-84, answer the given everyday math word problems.
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?

A right trapezoid is shown.
Figure 6P.2.7

Exercises: Writing Exercises

Instructions: For questions 85-88, answer the given 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 rectangle is shown on the left. It is labeled as 2 by 8. A square is shown on the right. It is labeled as 4 by 4.
Figure 6P.2.8

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?

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Fanshawe Pre-Health Sciences Mathematics 1 Copyright © 2022 by Domenic Spilotro, MSc is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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