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Circle in a Square

GRE-EXANIG

A circle with circumference 4 cm and radius $r$ is inscribed inside a square as shown in the figure.

What is the area of the shaded region in the figure?

A

$16 \pi \text{ cm}^2$

B

$\cfrac{16 - 4 \pi}{\pi} \text{ cm}^2$

C

$16 \text{ cm}^2$

D

$\cfrac{4 - 4 \pi}{\pi^2} \text{ cm}^2$

E

$\cfrac{16 - 4 \pi}{\pi^2} \text{ cm}^2$