Beautiful Geometry 1

Rectangles and Triangles

The area of the yellow triangle is 15. What’s the total orange area?

Let the two rectangles be ABCD and BEFG. Let H be the intersection of GD and FC. HECD is a trapezoid and therefore the triangles IEC and IDH formed by its diagonals have equal areas. Similarly, the triangles JCE and JFG in the trapezoid EFGC have equal areas.

Therefore, we have:

S(DHI) + S(FGJ) = S(JCE) + S(CIE) = S(JIE) = 15.