Color the indicated regions dark gray:

Now if we add the dark gray regions to the black region, we get triangle BCF, whose area is half that of the whole square (a triangle’s area is one-half base times height). If we add the dark gray areas to the light gray areas, we again produce a region that’s half the area of the square (because it’s the full square minus triangle ABE). So the black part and the light gray part are equal.

By V. Proizvolov, from the Russian science magazine Kvant.