Question

Find the ratio of area of an equilateral triangle and its circumcircle, if the side of a triangle is √3 cm.
1. 3√3/4 : π
2. 2√2/3 : π
3. 3√7/3 : π
4. 7√7/3 : π

Answer 1

Correct Answer - Option 1 : 3√3/4 : π

Given:

Side of an equilateral triangle is √3 cm.

Formula used:

Area of an equilateral triangle = √3(side)²/4

Radius of circumcircle of an equilateral triangle = side/√3

Calculation:

Area of an equilateral triangle = √3(√3)²/4

⇒ √3(3)/4

Radius of circumcircle = √3/√3

⇒ 1 cm

Area of circumcircle = π(1)²

⇒ π cm²

Required ratio = 3√3/4 : π

∴ The required ratio is 3√3/4 : π