Notes
two semi-circles inside a rectangle solution

Two Semi-Circles Inside a Rectangle

Solution by Circle Geometry

With the points labelled as in the above diagram, quadrilaterals $C D E F$ and $A B C F$ are kites, so $D C$ and $C F$ have the same length, as to $B C$ and $C F$. Therefore, $B C$ and $D C$ have the same length. The area of the white triangle is therefore one quarter of the area of the rectangle and so $\frac{3}{4}$ of the rectangle is shaded.