How many squares are there in the given figure?

The correct answer is Option (2) → 91

The figure is a grid of 6 × 6 small squares. A square of side \(k\) small squares can start at \(7-k\) places across and \(7-k\) places down, so there are \((7-k)^2\) squares of each size.

• 1 × 1 squares: \(6^2=36\)

• 2 × 2 squares: \(5^2=25\)

• 3 × 3 squares: \(4^2=16\)

• 4 × 4 squares: \(3^2=9\)

• 5 × 5 squares: \(2^2=4\)

• 6 × 6 square: \(1\)

• Total: \(36+25+16+9+4+1=91\)

Shortcut:

• An \(n\times n\) grid has \(1^2+2^2+\ldots+n^2=\frac{n(n+1)(2n+1)}{6}\) squares.

• For \(n=6\): \(\frac{6\times7\times13}{6}=91\)