בס’ד
In geometry, there is a Theorem that for a right-sided triangle, that the length of the Hypotenuse (the long slanted side) when squared is the sum of the squares of the lengths of the bases and heights of the triangle.
Oddly enough, in geometry class, rarely is this Theorem actually proven, although the proof is simple!
The proof of the theorem is graphically presented here (two simple proofs):
I came up with these proofs (and a third one, just cutting the "c" by "c" square in the top picture diagonally) when one of my children asked me about it and started the concepts on the paper, completing her thought of relating the areas with an actual implementation or two.
There is more information about the theorem here:
http://en.wikipedia.org/wiki/Pythagorean_theorem