2013 AMC8 Problem 20

bridge

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

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