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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.
Solution
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
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