Question

In the chessboard if the rectangle form is 1296, find the total number of squares formed.

Answer 1

To find the total number of squares formed on a chessboard, including all sizes from 1x1 up to the largest square, you can use the following formula:
Total number of squares = \(\frac{(n^4+n^3+n^2)}{6}\)
In this case, since the rectangle has an area of 1296, we can find the length of one side by taking the square root of 1296:
Side length = √1296 = 36
Now we can substitute the value of n into the formula:
Total number of squares = \(\frac{(36^4+36^3+36^2)}{6}\)
Calculating this expression:
Total number of squares = \(\frac{(1296+11664+1296)}{6}\) = \(\frac{14256}{6}\) = 2376
Therefore, on a chessboard where the rectangle formed has an area of 1296, the total number of squares formed is 2376.