The problem asks us to determine how many rectangles can be formed on a standard chessboard.

A standard chessboard is an 8x8 grid. To find the number of rectangles in a grid, we use the formula:

\(R = \frac{n(n+1)m(m+1)}{4}\)

where \(n\) and \(m\) are the number of rows and columns, respectively. For an 8x8 chessboard, both \(n\) and \(m\) are 8.

Substituting into the formula:

\(R = \frac{8(8+1)8(8+1)}{4}\)

\(R = \frac{8 \cdot 9 \cdot 8 \cdot 9}{4}\)

\(R = \frac{5184}{4}\)

\(R = 1296\)

Therefore, the total number of rectangles on a chessboard is 1296.

This matches the given correct answer option:

• 1296