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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 into the form of a circle, what will be the area of the circle? [Take π = 22/7]
Let the sides of equilateral triangle be a cm
Area of equilateral triangle = 121√3 cm2
Area of equilateral triangle = √3/4 × a2
⇒ √3/4 a2 = 121√3
⇒ a2 = 121√3 × 4/√3 = 121 × 4 cm2
⇒ a2 = 484 cm2
⇒ a = 22 cm
Perimeter of equilateral triangle = 3a
= 3 × 22 cm = 66 cm
Perimeter of equilateral triangle = Circumference of circle
Circumference of circle = 66 cm
Let the radius of circle be r
Circumference of circle = 2πr
⇒ 2πr = 66 cm
⇒ 2 × 22/7 × r = 66 cm
⇒ r = 66 × 1/2 × 7/22 cm
⇒ r = 10.5 cm
Area of circle = πr2 = 22/7 × 22/7 × 10.5 × 10.5 cm2
= 346.5 cm2