A SIMPLE CHESS MATH GAME

First of all, lets make this chessboard into 9 * 9 lined board like this!

We need to choose two vertical lines and two horizontal lines to make a rectangle. Since there are 9 lines horizontally and vertically, it would be ... $\binom{9}{2} * \binom{9}{2} = \binom{9}{2} ^ {2} = 1296$

However, this includes the squares too. So we need to find the number of squares, and we do that two ways. We can realize that the sum of all the squares is in the form where n is the length of the square...

$n^{2} + (n-1)^ {2} + (n-2)^{2}+ ... + 1$

or know the formula for the number of squares in a square...

$\frac{n\times (n+1)\times(2n+1)}{6}$

Therefore, the number of squares is $204$ . So then take away the included squares in the rectangle amount we got $1296-204=1092$ and put the $1092$ and the $204$ together in the form rectangle.square. $\boxed {1092.204}$