# Solution to the Overlapping Triangles Puzzle +-- {.image} [[OverlappingTriangles.png:pic]] > When I place two $3-4-5$ triangles like this, what's the overlapping area? =-- ## Solution by Properties of a [[Rectangle]] +-- {.image} [[OverlappingTrianglesLabelled.png:pic]] =-- In the above diagram, $A B C D$ is a rectangle. Since angle $B \hat{A} F$ is the same as angle $D \hat{B} A$ as the triangles are [[similar]], so $A F$ lies along the diagonal of the rectangle and $A F C$ is a straight line. The point $G$ is where the diagonals cross so is the centre of the rectangle. Therefore triangle $A B G$ is a quarter of the rectangle. As the sides of the rectangle are $3$ and $4$, its area is $12$ so the overlapping region has area $3$.