Notes
two overlapping squares solution

Solution to the Two Overlapping Squares Puzzle

Solution by Pythagoras' Theorem and Similar Triangles

Let the two squares have side lengths $a$ and $b$, with $a$ for the light blue and $b$ for the dark blue. Applying Pythagoras' theorem to triangle $A B C$ shows that:

Triangle $A E D$ is similar to triangle $A B C$ with scale factor $\frac{a}{b}$, so the length of $A E$ is $\frac{a^2}{b}$. The area of the shaded region is then given by: