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