Mensuration-32

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A wire when bent in the form of an equilateral triangle encloses an area of 121 √3 cm2.
If the same wire is bent in the form of a circle, find the area of the circle.

Solution: Given area of the equilateral triangle = 121 √3 cm2

=> √3 / 4 x a2 = 121 √3, where a is the side of the triangle

=> a2 = 484; a = √484 = 22 cm.

The same wire is bent in the form of a circle

=> Circumference of the circle = Perimeter of the equilateral triangle

=> 2 Π r = 3 x a, where r is the radius of the circle

2 Π r = 66

=> r = (66 x 7) / (2 x 22) = 10.5 cm

Hence, area of the circle = Π r2 = (22 / 7 x 10.5 x 10.5) cm2 = 346.5 cm2

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