pythagoras

An illustration of Pythagoras' theorem. Four identical right-angled triangles of cardboard are put in a square tray with the right angles in the corners. The sum of the two shorter sides must be equal to the side of the tray. The uncovered area of tray is the square of the hypotenuse.
The triangles can also be put together to form two rectangles; the uncovered area is the sum of the squares on the other two sides