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

1.	The perimeter of a regular hexagon and an equilateral triangle is same. What will be the ratio of their areas.1. 2 : 32. 6 : 1 3. 3 : 24. 3 : 1
Answer» 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.

The perimeter of a regular hexagon and an equilateral triangle is same. What will be the ratio of their areas.1. 2 : 32. 6 : 1 3. 3 : 24. 3 : 1

Answer» 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.

Discussion

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