Question

How many squares are there in the following figure?

Answer 1

Each side of the bigger square is divided into three equal parts.Apply the formula: If a square is divided into 'n' parts on each side, then the total number of squares formed = $\frac{n(n+1)(2n+1)}{6}$
Here the value of n = 3.
So, the total number of square = $\frac{3(3+1)(2\times 3+1)}{6}=\frac{3\left(4\right)\left(7\right)}{6}=\frac{1\times 84}{6}=14$
(Or to be simple, add $1^2+2^2+3^2=1+4+9)$
Square at the four corners = $4\times 2=8$
Square formed at the centre = 1.
Total number of square = 14 + 8 + 1 = 23.