Question

The diameter of a coin is 1 cm(Fig). 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 $\pi =3.1416$)

Answer 1

Given,
Diameter of a coin = 1cm

Radius = $\frac{diameter}{2}$

= $\frac{1}{2}$

= 0.5 cm

If the centres are connected with each other creating a quadrilateral,
we will get a square of side = 1cm
So area of square = ( side) x (side )
= 1 x 1
= 1 $c{m}^2$

In this square , we find four quadrants including the unoccupied space.

Radius of each quadrant = $\frac{1}{2}$

Area of 1 quadrant = $\frac{22}{7}$ . $\frac{1}{2}$ . $\frac{1}{2}$ . $\frac{1}{4}$

= 0.196 approx $c{m}^2$

Area of 4 quadrants = 0.786 approx. $c{m}^2$

Area of unoccupied space = 1$c{m}^2$- 0.786 $c{m}^2$

= 0.214 $c{m}^2$

=0.2 $c{m}^2$