Question

An equilateral triangle and a regular hexagon have the same perimeter. The ratio of the area of the triangle to that of the hexagon is
1. 3 : 2
2. 2 : 3
3. 1 : 2
4. 1 : 4

Answer 1

Correct Answer - Option 2 : 2 : 3

Let perimeter of the triangle and regular hexagon be 6 unit.

Side of the triangle = 6/3 = 2 cm

Side of the hexagon = 6/6 = 1 cm

As we know,

Area of triangle = (√3/4) × a² = (√3/4) × 2 × 2 = √3

Area of hexagon = 6 × (√3/4) × a² = 6 × (√3/4) × 1 × 1 = 3√3/2

Ratio of area of triangle to that of the hexagon = √3 : 3√3/2 = 2 : 3