Question

A wire bent in the form of an equilateral triangle has an area of `121sqrt(3)"cm"^2`. If the same wire is bent into the form of a circle, find the area enclosed by the wire.

Answer 1

We know that, Area of an equilateral triangle(A) of side a is A = `sqrt(3)/(4)"a"^2`
Here, A = `121sqrt(3)`

⇒ `121sqrt(3) = sqrt(3)/(4)"a"^2`

⇒ 121 = `"a"^2/(4)`

⇒ 11 = `"a"/(2)`

⇒ a = 22
⇒ 3a = 66cm
The Circumference of a Circle with radius r = 2πr
Here,
66cm = 2πr
⇒ 66
⇒ r = 10.5cm
The Area of a Circle with radius r = πr²
The Area of a Circle with radius 10.5

= `(22)/(7)(10.5)^2`
= 346.5cm².