20. Given a rectangle $A B C D$ with a length of 2 and a width of 1 inscribed in a semicircle $\odot O$, and the length $B C$ of the rectangle lies on the diameter of the semicircle. Then the area of the semicircle $\odot 0$ is ( ).
(A) $\frac{\pi}{2}$
(B) $\frac{2 \pi}{3}$
(C) $\pi$
(D) $\frac{4 \pi}{3}$
(E) $\frac{5 \pi}{3}$
20. C.

As shown in Figure 7.
Since rectangle $A B C D$ is inscribed in the semicircle $\odot O$, we have $O B=O C=\frac{1}{2} B C=1$.

Also, $C D=1$, so $O D=\sqrt{2}$.
Therefore, $S_{\text {semicircle }}=\frac{1}{2} \times(\sqrt{2})^{2} \pi=\pi$.