Question

In the following figure, ABC is an equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of radius 4 cm. Find the area of the shaded region correct upto 2 decimal places. (Take π =3.142 and`sqrt3` = 1.732).

Answer 1

Area of the shaded region can be calculated as shown below,

Area of the shaded region = Area of equilateral triangle − 3` xx`area of circular arc

`"∴ Area of the shaded region" = sqrt3/4 xx 8 xx 8-3 xx 60/360 xx pi xx 4 xx 4`

`"∴ Area of the shaded region"=sqrt3 xx 2 xx 8-3 xx 1/6 xx pi xx 4 xx 4`

`"∴ Area of the shaded region" = sqrt3 xx 16 - 1/2 xx pi xx 16`

`"∴ Area of the shaded region" = sqrt3 xx 16 - pi xx 8`

Substituting sqrt`3 = 1.732` and `pi = 3.142`we get,

`"∴ Area of the shaded region" = 1732 xx 16 - 3.142 xx 8`

`"∴ Area of the shaded region" = 27.712 - 25.136`

`"∴ Area of the shaded region" = 2.576`

Therefore, area of the shaded region is `2.576  cm^2`