imc

Since the area of the square is $40$, the length of a side is $\sqrt{40}=2\sqrt{10}$. The distance between the center of the semicircle and one of the bottom vertices of the square is half the length of the side, which is $\sqrt{10}$. Using the Pythagorean Theorem to find the radius $r$ of the semicircle, $r^2=(2\sqrt{10}{)}^2+(\sqrt{10}{)}^2=50$. So, the area of the semicircle is $\frac{1}{2}\cdot \pi \cdot 50=\boxed{25\pi }$.