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"=sqrt3/4xx8xx8-3xx60/360xxpixx4xx4`

`"∴ Area of the shaded region"=sqrt3xx2xx8-3xx1/6xxpixx4xx4`

`"∴ Area of the shaded region"=sqrt3xx16-1/2xxpixx16`

`"∴ Area of the shaded region"=sqrt3xx16-pixx8`

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

`"∴ Area of the shaded region"=1732xx16-3.142xx8`

`"∴ 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`