Notes
triangles formed from rectangles solution

Solution to the Triangles Formed from Rectangles Puzzles

Solution by Crossed Trapezium

In the above diagram, the line $B E$ defines two trapeziums: $A B E F$ with $A B$ parallel to $F E$, and $B C D E$ with $B C$ parallel to $E D$. In each trapezium the shaded areas are the side triangles in a crossed trapezium and therefore are of equal area. Put together, the total orange area is the same as the yellow area and so is $15$.