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The area of each square on a chess board is 4 sq cm. Find the area of the board.

(a) At the beginning of game when all the chess men are put on the board, write area of the squares left unoccupied.

(b) Find the area of the squares occupied by chess men.

Answer:

We know that, there are 64 squares in a chess board.

Given area of each square of chess board \[=4c{{m}^{2}}\]

\[\therefore\] Area of the board = Number of square in a

board \[\times\] Area of one square

\[=64\times 4\text{ }cm=256\text{ }c{{m}^{2}}\]

(a) We know that in a game of chess, there are two players each of row 16 chess men.

Now, total number of squares occupied by the chess men in the board

\[=16\times 2=32\]

\[\because\] Total number of squares are unoccupied by the chess men in the board are

= Total number of squares in a chess board ? Number of squares occupied by the chess men in the board

\[=64-32=32\].

\[\therefore\] The area of the squares unoccupied

= Number of squares left unoccupied by the chess men \[\times\] area of one square

\[=32\times 4\text{ }cm=128\text{ }c{{m}^{2}}\]

(b) The area of the squares occupied by chess men = Number of square occupied by chess board \[\times\] Area of one square

\[=32\times 4\text{ }cm=128\text{ }c{{m}^{2}}\].