16. A semicircle is drawn on each side of a square, as shown.
The square has sides of length $2 \pi$.
What is the area of the resulting shape?
A $2 \pi^{2}(\pi+1)$
B $\pi^{2}(\pi+2)$
C $2 \pi^{2}(2 \pi+1)$
D $\pi^{2}(\pi+4)$
E $2 \pi^{2}(\pi+2)$
16. E The square has sides of length $2 \pi$, so its area is $(2 \pi)^{2}=4 \pi^{2}$. Each of the four semicircles has radius $\pi$, hence the sum of the areas of the semicircles is $4 \times \frac{1}{2} \times \pi \times \pi^{2}=2 \pi^{3}$.
Therefore the required area is $2 \pi^{3}+4 \pi^{2}=2 \pi^{2}(\pi+2)$.