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 π (no approximations).

Answer 1

The perimeter = 4 * length of a semicircle of radius 5 == 4*  pi * 5 =  20 pi cm



The area of one of the clear parts = 1/2 area of square - area semicircle

= 1/2 * 10^2  -  1/2 pi *5^2 = 50 - 12.5pi 

So area of shaded parts =  area of square -  4 (50 - 12.5pi)
 = 100 - 200 + 100pi = (100pi - 100) cm^2