Question

7 a playground is in the shape of an isosceles trapezoid. the top base is 10 ft. the bottom base is 42 ft. the height is 12 ft. a slanted side is 20 ft. what is the distance around the playground?
8 one part of the roof of a house is in the form of an isosceles trapezoid. the bottom base is 28 feet long. the top base is 6 feet long, and the height is 16 feet. what is the area of this portion of the roof?
9 a place mat is in the form of an isosceles trapezoid. one base of the trapezoid is 17 inches long, and the other base is 13 inches long. the height is 12 inches. what is the area of the place mat?

Explanation:

Step1: Identify the formula for the perimeter of an isosceles trapezoid

The perimeter \(P\) of a trapezoid is \(P = a + b+ 2c\), where \(a\) and \(b\) are the lengths of the bases and \(c\) is the length of the non - parallel (slanted) side.

Step2: Substitute the given values into the formula

Given \(a = 10\) ft (top base), \(b = 42\) ft (bottom base), and \(c = 20\) ft (slanted side).

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Step1: Identify the formula for the area of a trapezoid

The area \(A\) of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the bases and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(a = 6\) ft (top base), \(b = 28\) ft (bottom base), and \(h = 16\) ft (height).

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Step1: Identify the formula for the area of a trapezoid

The area \(A\) of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the bases and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(a = 13\) inches (one base), \(b = 17\) inches (the other base), and \(h = 12\) inches (height).

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Answer:

The distance around the playground (perimeter) is \(92\) ft.

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