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).

 

Answer 1

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`