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

First compute the area of the square like this:
`9^2=81`
There is two semi circles here, so the sum of the two white
spaces equate the area of a circle.
the radius of the circle is 9/2.
So compute the area of the like this:
`\pi ((9)/(2))^2`
And the area of the shaded region is the area of the square minus
the area of the two semi circles, like this:

`81-\pi ((9)/(2))^2`
We are done.