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17. Find the area of the shaded
portion of this figure, which
consists of a parallelogram
enclosing a right triangle
and a circle. Dimensions are
in feet. (Round off answer to
the nearest tenth of a foot.)


8 17. Find the area of the shaded portion of this figure, which consists of a parallelogram-example-1

1 Answer

4 votes

Answer:

37.4 ft^2

Explanation:

The area of the parallelogram is given by ...

A = bh = (8 ft)(7 ft) = 56 ft^2

The area of the right triangle is given by ...

A = (1/2)bh = (1/2)(3 ft)(4 ft) = 6 ft^2

The area of the circle is given by ...

A = πr^2 = π(2 ft)^2 = 4π ft^2 ≈ 12.6 ft^2

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The shaded area is the area of the parallelogram less the areas of the unshaded triangle and circle:

(56 ft^2) -(6 ft^2) -(12.6 ft^2) = 37.4 ft^2 . . . . shaded area

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