Notes
semi-circles in a square solution

Semi-Circles in a Square

Solution by Dissection

In the above diagram, the regions outside the square are equal in area to the purple regions inside, so the shaded region has area equal to half that of the square. As the radius of each semi-circle is $5$, the diameter of the square is $20$ and so its area is $200$. The shaded region therefore has area $100$.