Question

Find the number of rectangles an and Squares in chess 8 by 8 board respectively.​

Answer 1

squares: 204

rectangle: 1,296

Explanation:

Board Size: 8 x 8

The total number of squares is thus:

`1^(2) + 2^(2) + ... + n^(2)`

sum =
`(n(n + 1)(2n + 1))/(6)`

For a chess board, with n = 8,

sum =
`((8)((8) + 1)(2(8) + 1))/(6)`

sum = 204

the number of rectangles on a chess board,

to make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. There are 36 distinct pairs and the same number of vertical pairs, so the answer is 36 × 36 = 1,296.