Check the picture below.
so, if we can just get the total area of the shaded semicircle, and then get the combined area of the 3 smaller semicircles, so if we subtract the combined area of the smaller semicircles from the larger one, what's left is the shaded area, by subtracting the area of the smaller ones, is pretty much like making 3 holes in the area of the shaded semicircle.
[tex]\stackrel{\textit{area of the shaded semicircle}}{\cfrac{1}{2}\pi (15)^2\implies \cfrac{225\pi }{2}} ~\hfill \stackrel{\textit{combined area of the 3 small semicircles}}{3\left[\cfrac{1}{2}\pi (5)^2 \right]\implies \cfrac{75\pi }{2}} \\\\\\ \cfrac{225\pi }{2}-\cfrac{75\pi }{2}\implies 75\pi \implies 75(3.14)\implies 235.5~cm^2[/tex]
