jmc

From smallest to largest, the semicircles have radii of 2, 4, 6, and 8 cm, respectively. Each has area $\frac{r^2}{2}\pi$, so from smallest to largest the semicircles have area $2\pi$, $8\pi$, $18\pi$, and $32\pi$ sq cm, respectively. The shaded area is that of the largest minus the second largest, plus the second smallest minus the smallest, so the total area is $32\pi -18\pi +8\pi -2\pi =20\pi$ sq cm, which rounds to $\boxed{62.8}$ sq cm.