Notes
areas in a crossed trapezium solution

Solution to the Areas in a Crossed Trapezium Puzzle

Solution by Crossed Trapezium

As shown on the page on crossed trapezium, the two blue triangles have the same area and the area scale factor from the white triangle to each of the blues is the same as from each of the blues to the purple. Since the purple triangle has twice the area of each blue, each blue therefore has twice the area of the white and the purple has four times the area of the white. The full trapezium is nine ($4 + 2 + 2 + 1$) times the size of the white triangle, so $\frac{8}{9}$ths of it is shaded.