Question

A wire bent in the form of an equilateral triangle has an area of 121 `sqrt 3` cm². If the same wire is bent into the form of a circle , find the area enclosed by the wire.

Answer 1

Area of equi I ater al triangle = 121 `sqrt 3` cm² 

`=> ("s"^2 sqrt 3)/4 = 121 sqrt 3`

`=> "s"^2 - 484`

`=> "s" = 22 "cm"`

Side of the triangle = 22 cm 

Perimeter of the triangle= 3 x 22 = 66 cm 

Perimeter of the circle = perimeter of the triangle 

`=> 2 pi "r" = 66`

`=> "r" = 66 xx 7/22 xx 1/2`

⇒ r = 10.5 cm

Radius of circle = 10.5 cm 

Area of cirde = π r² 

`= 22/7 xx 10.5 xx 10.5`

= 346.5 cm²

Hence, area of the circle = 346.5 cm²