Question

The perimeter of a regular hexagon and an equilateral triangle is same. What will be the ratio of their areas.
1. 2 : 3
2. 6 : 1 
3. 3 : 2
4. 3 : 1

Answer 1

Correct Answer - Option 3 : 3 : 2

Given-

The perimeter of a regular hexagon and an equilateral triangle is same.

Concept Used-

Area of equilateral triangle = √3/4 × Side²

Area of a regular hexagon = 3√3/2 × Side²

Calculation- 

Let the perimeter of the triangle and hexagon be 6a

Each Side of Hexagon = a

Each Side of Triangle = 2a

Area of Hexagon = 3√3/2 × a²

Area of Triangle = √3/4 × (2a)2

⇒ √3a²

∴ The ratio of their areas = (3√3/2 × a²) : (√3a²)

⇒ 3 : 2

∴ The required ratio will be 3 : 2.