Hooper's paradox

This means, the real triangles of the original shape overlap in the rectangle.

The overlapping area is a parallelogram, the diagonals and sides of which can be computed via the Pythagorean theorem.

The area of this parallelogram can determined using Heron's formula for triangles.

William Hooper published the paradox in 1774 in his book Rational Recreations, calling it "The geometric money".

However Hooper was not the first to publish this geometric fallacy, since Hooper's book was largely an adaption of Edmé-Gilles Guyot's Nouvelles récréations physiques et mathétiques, which had been published in France in 1769.