Question

The following three shapes are based only on squares, semicircles, and quarter circles.

Find the perimeter and the area of each shaded part. Give your answer as a completely
simplified exact value in terms of pie (no approximations).

Answer 1

32pi - 64

Explanation:

The two UNshaded areas are equal to each other. Each one is the

Area (square) - 1/4 Area(circle)

64 - 1/4 (64pi)

64 - 16pi

There are 2 of these unshaded pieces in this question.

Area (square) - 2 (64 - 16pi)

64 - 128 + 32pi

= -64 + 32pi

Area = 32pi - 64