# Mensuration-32

### From Homeworkwiki

**A wire when bent in the form of an equilateral triangle encloses an area of 121 √3 cm ^{2}.**

**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 cm^{2}

=> √3 / 4 x a^{2} = 121 √3, where a is the side of the triangle

=> a^{2} = 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 r^{2} = (22 / 7 x 10.5 x 10.5) cm^{2} = 346.5 cm^{2}