Notes
overlapping triangles solution

Solution to the Overlapping Triangles Puzzle

Solution by Properties of a Rectangle

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 $3$.