AMC 8 2013 Problem 20

A $1\times 2$ rectangle is inscribed in a semicircle with the longer side on the diameter. What is the area of the semicircle? $\textbf{(A)}\ \frac\pi2 \textbf{(B)}\ \frac{2\pi}3 \textbf{(C)}\ \pi \textbf{(D)}\ \frac{4\pi}3 \textbf{(E)}\ \frac{5\pi}3$