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Question
The diameter of a coin is 1 cm (in the following figure). If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region (Take π = 3.1416).
Solution
Look at the figure carefully shaded region is bounded between four sectors of the circle with same radius and a square of side 1 cm.
Therefore, the area of the shaded region is nothing but the difference the area of the square and area of one circle.
`"∴ Area of the shaded region=Area of square-Area of a circle"`
`"∴ Area of the shaded region"=1^2-pi (0.5^2)`
`"∴ Area of the shaded region"=1-0.25pi`
Substituting `pi=3.1416` we get,
`"∴ Area of the shaded region"=1-3.1416xx0.25`
`"∴ Area of the shaded region"=1-0.7854`
`"∴ Area of the shaded region"=0.2146`
Therefore, area of the shaded region is `0.2146cm^2`
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