The perimeter of a square with a side of length S is equal to the circumference of a circle. In terms of S, what is the area of the circle?

Two ways

(I). Geometric
Perimeter of square = 4S = $2\pi*r..........r=\frac{2S}{\pi}....Area = \pi*r^2=\pi(\frac{2S}{\pi})^2=\frac{4S^2}{\pi}$

(II) take S as $\pi$
so perimeter = 4$\pi$=circumference = $2\pi*r=4\pi.....r=2.......Area = \pi*r^2=4\pi$
check choices
A. $\frac{S^4}{4\pi}......\frac{\pi^4}{4\pi}=\pi^3/4$...no

B. $\frac{s^2}{\pi}.....\frac{\pi^2}{\pi}=\pi$...no

C. $\frac{4s^2}{\pi^2}.....\frac{4\pi^2}{\pi^2}=4$....no

D. $\frac{4s^2}{\pi}.......\frac{4\pi^2}{\pi}=4\pi$...yes

E. $\frac{4s}{\pi}.........\frac{4\pi}{\pi}=4$....no

D