# Solution to the [[Four Squares X]] Puzzle +-- {.image} [[FourSquaresX.jpg:pic]] > Four squares. What’s the blue square’s area? =-- ## Solution by Properties of [[Right-Angled Triangles]] and [[Squares]] +-- {.image} [[FourSquaresXLabelled.png:pic]] =-- 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 $18$.