How many rectangles are in a checker board?

There are 1296 rectangles on a checker board.

There are 64 different sized rectangles: 1x1, 1x2, 1x3 ... 1x8, 2x1, 2x2 2x3 ... 8x8. The number of a (axb) sized rectangle is (9-a)*(9-b). Thus, there are 64 1x1 rectangles, 56 1x2 rectangles, etc. Adding all these numbers gives 1296. (1296 also happens to be 6 to the power of 4. Coincidence?) Of these 1296 rectangles, 204 of them are squares.