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Use the Properties of Trapezoids
In the following exercises, solve using the properties of trapezoids.
The height of a trapezoid is $12$ feet and the bases are $9$ and $15$ feet. What is the area?
144 sq. ft
The height of a trapezoid is $24$ yards and the bases are $18$ and $30$ yards. What is the area?
Find the area of a trapezoid with a height of $51$ meters and bases of $43$ and $67$ meters.
2805 sq. m
Find the area of a trapezoid with a height of $62$ inches and bases of $58$ and $75$ inches.
The height of a trapezoid is $15$ centimeters and the bases are $12.5$ and $18.3$ centimeters. What is the area?
231 sq. cm
The height of a trapezoid is $48$ feet and the bases are $38.6$ and $60.2$ feet. What is the area?
Find the area of a trapezoid with a height of $4.2$ meters and bases of $8.1$ and $5.5$ meters.
28.56 sq. m
Find the area of a trapezoid with a height of $32.5$ centimeters and bases of $54.6$ and $41.4$ centimeters.
Laurel is making a banner shaped like a trapezoid. The height of the banner is $3$ feet and the bases are $4$ and $5$ feet. What is the area of the banner?
13.5 sq. ft
Niko wants to tile the floor of his bathroom. The floor is shaped like a trapezoid with width $5$ feet and lengths $5$ feet and $8$ feet. What is the area of the floor?
Theresa needs a new top for her kitchen counter. The counter is shaped like a trapezoid with width $18.5$ inches and lengths $62$ and $50$ inches. What is the area of the counter?
1036 sq. in.
Elena is knitting a scarf. The scarf will be shaped like a trapezoid with width $8$ inches and lengths $48.2$ inches and $56.2$ inches. What is the area of the scarf?
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 $50$ foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be $10$ feet. How long can he make the other side if he wants to use the entire roll of fence?
15 ft
Gardening Lupita wants to fence in her tomato garden. The garden is rectangular and the length is twice the width. It will take $48$ feet of fencing to enclose the garden. Find the length and width of her garden.
Fence Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are $6$ feet, $8$ feet, and $10$ feet. The fence costs $\mathrm{\$10}$ per foot. How much will it cost for Christa to fence in her flowerbed?
$24
Painting Caleb wants to paint one wall of his attic. The wall is shaped like a trapezoid with height $8$ feet and bases $20$ feet and $12$ feet. The cost of the painting one square foot of wall is about $\mathrm{\$0.05}.$ About how much will it cost for Caleb to paint the attic wall?
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.
Answers will vary.
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.
Look at the two figures.
ⓐ Which figure looks like it has the larger area? Which looks like it has the larger perimeter?
ⓑ Now calculate the area and perimeter of each figure. Which has the larger area? Which has the larger perimeter?
Answers will vary.
The length of a rectangle is $5$ feet more than the width. The area is $50$ square feet. Find the length and the width.
ⓐ Write the equation you would use to solve the problem.
ⓑ Why can’t you solve this equation with the methods you learned in the previous chapter?
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?
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