Notes
four squares x solution

Solution to the Four Squares X Puzzle

Solution by Properties of Right-Angled Triangles and Squares

In the diagram labelled as above, $C D A$ is a straight line so triangle $C B A$ is a right-angled triangle with $D$ as the midpoint of its hypotenuse. Therefore, by the properties of right-angled triangles, line segment $B D$ has the same length as $D A$. Then from the properties of squares, the blue square has twice the area of each of the yellow squares, so has area $18$.