1982 AHSME Problem 4

The perimeter of a semicircular region, measured in centimeters, is numerically equal to its area, measured in square centimeters. The radius of the semicircle, measured in centimeters, is

\text{(A)} \pi \qquad \text{(B)} \frac{2}{\pi} \qquad \text{(C)} 1 \qquad \text{(D)}\frac{1}{2}\qquad \text{(E)}\frac{4}{\pi}+2

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.