How many squares can be formed out of a chess board?Choices:- 196 204 225 250

The chess board is an 8x8 grid. To find out how many squares can be formed, we need to consider squares of all possible sizes that can be formed on the board.

1x1 squares: There are 8 squares per row, and 8 squares per column, so there are 8*8 = 64 1x1 squares.

2x2 squares: There are 7 squares per row, and 7 squares per column, so there are 7*7 = 49 2x2 squares.

3x3 squares: There are 6 squares per row, and 6 squares per column, so there are 6*6 = 36 3x3 squares.

4x4 squares: There are 5 squares per row, and 5 squares per column, so there are 5*5 = 25 4x4 squares.

5x5 squares: There are 4 squares per row, and 4 squares per column, so there are 4*4 = 16 5x5 squares.

6x6 squares: There are 3 squares per row, and 3 squares per column, so there are 3*3 = 9 6x6 squares.

7x7 squares: There are 2 squares per row, and 2 squares per column, so there are 2*2 = 4 7x7 squares.

8x8 squares: There is 1 square per row, and 1 square per column, so there is 1*1 = 1 8x8 square.

Adding all these up, we get 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 squares. So, the correct answer is 204.

The chess board has 8 rows and 8 columns.

1. A 1x1 square can be formed in 8 rows * 8 columns = 64 ways.
2. A 2x2 square can be formed in 7 rows * 7 columns = 49 ways.
3. A 3x3 square can be formed in 6 rows * 6 columns = 36 ways.
4. A 4x4 square can be formed in 5 rows * 5 columns = 25 ways.
5. A 5x5 square can be formed in 4 rows * 4 columns = 16 ways.
6. A 6x6 square can be formed in 3 rows * 3 columns = 9 ways.
7. A 7x7 square can be formed in 2 rows * 2 columns = 4 ways.
8. An 8x8 square can be formed in 1 row * 1 column = 1 way.

So, the total number of squares that can be formed out of a chess board is 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204.

So, the correct answer is 204.