gray area is equal to sum of black areas, trapezoid, parallelogram
Source: 2009 Oral Moscow Geometry Olympiad grades 10-11 p2
September 14, 2020
geometrytrapezoidareasparallelogram
Problem Statement
Trapezium and parallelogram are located so that the sides of the parallelogram are parallel to the diagonals of the trapezoid (see fig.). Prove that the area of the gray part is equal to the sum of the areas of the black part.(Yu. Blinkov)
https://cdn.artofproblemsolving.com/attachments/b/9/cfff83b1b85aea16b603995d4f3d327256b60b.png