2013 AMC 8 Problem 20

A 1\times 2 rectangle is inscribed in a semicircle with longer side on the diameter. What is the area of the semicircle?

\textbf{(A)}\ \frac\pi2 \qquad \textbf{(B)}\ \frac{2\pi}3 \qquad \textbf{(C)}\ \pi \qquad \textbf{(D)}\ \frac{4\pi}3 \qquad \textbf{(E)}\ \frac{5\pi}3

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