Question

An equilateral triangle is formed by a wire and its area is 36√3. If any circle is formed by the same length of the wire then what will be the area of the circle?
1. 181/π 
2. 324/π 
3. 49/π 
4. 225/π 

Answer 1

Correct Answer - Option 2 : 324/π 

Given:

The area of equilateral triangle = 36√3

Concept used:

The perimeter of triangle = circumference of a circle

Formula used:

Area of equilateral triangle = √3a²/4

where a is the side of the triangle 

Calculation:

Area of equilateral = √3a²/4

⇒ √3a²/4 = 36√3

⇒ a = 12

⇒ Perimeter of triangle = 3 × a = 36

Using concept

The perimeter of triangle = circumference of a circle

⇒ 36 = 2πr

⇒ 18/π = r

Area of circle = πr²

⇒ π × 18/π × 18/π

⇒ 324/π

∴ The area of the circle is 324/π.