jmc

Draw line $\overline{BD}$. Then draw $\overline{CO}$, where $O$ is the center of the semicircle. You have two quarter circles on top, and two quarter circle-sized "bites" on the bottom. Move the pieces from the top to fit in the bottom like a jigsaw puzzle. You now have a rectangle with length $\overline{BD}$ and height $\overline{AO}$, which are equal to $10$ and $5$, respectively. Thus, the total area is $50$, and the answer is $\boxed{50}$.