Answer / guest

There are 55 squares in a 5 by 5 grid.

There are 25 squares of one grid.

There are 16 squares of four grids i.e. 2 by 2

There are 9 squares of nine grids i.e. 3 by 3

There are 4 squares of sixteen grids i.e. 4 by 4

There is 1 square of twenty-five girds i.e. 5 by 5

Hence, there are total 25 + 16 + 9 + 4 + 1 = 55 squares.

You must have noticed one thing that total number squares
possible of each size is always a perfact square i.e. 25,
16, 9, 4, 1

For a grid of N by N, the possible number of squares are

= N2 + (N - 1)2 + (N - 2)2 + (N - 3)2 + ......... + 32 + 22
+ 12

For 1 by 1 grid, total squares = 12 = 1

For 2 by 2 grid, total squares = 22 + 12 = 5

For 3 by 3 grid, total squares = 32 + 22 + 12 = 14

For 4 by 4 grid, total squares = 42 + 32 + 22 + 12 = 30

For 5 by 5 grid, total squares = 52 + 42 + 32 + 22 + 12 = 55

Answer / savita

55
there is a formula summation of n2(n square)
hence 1^2 + 2^2 + 3^2 + 4^2 +5^2
=1 + 4 + 9 + 16 + 25
=55

Answer / shadow

There are 55 squares in 5 inch by 5 inch grid.

Answer / thirumurugan

25

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