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Question

How many rectangles are there in the chessboard?

The correct answer is
1296

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
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Important Questions from Counting Figures

  1. How many triangles are there in the given figure?

  2. Find the number of squares in the given figure. ( Rectangles NOT to be included ).

  3. Find the number of triangles in the given figure.

  4. How many triangles are there in the question figure?

  5. How many triangles are there in the question figure?

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