How many rectangles are there in the chessboard?

Question

Question

This question was previously asked in

UP Police Constable Re-Exam 2024 Official Paper (Held On: 25th Aug 2024 Shift 1)

Answer 1

The number rectangles in the chessboard are shown below:

qImage66ce3774578808195d07cd69

So, Chessboard has 8 squares vertically and 8 horizontally.

Now, to calculate the number of rectangles :

Formula → $[\frac{n (n + 1)}{2}]^{2}$

where, n = 8

→ $[\frac{8 (8 + 1)}{2}]^{2}$

→ $[\frac{8 \times 9}{2}]^{2}$

→ $[\frac{72}{2}]^{2}$

→ (36)²

→ 1296

∴ There are 1296 rectangles in the chessboard.

Hence, "1296" is the correct answer.