Notes
three squares on a line solution

Three Squares on a Line

Solution by Properties of a Square

As $C B G D$ is a square, the height of $C$ above $A B$ is the same as that of $D$ above $G H$, similarly that of $C$ above $D E$ is the same as of $B$ above $F G$. The side lengths of the two blue squares are $2\sqrt{5}$ and $3\sqrt{5}$, so the area of each of the triangles is $\frac{1}{2} \times 2\sqrt{5} \times 3\sqrt{5} = 15$ which means that the area of the shaded region is $30$.