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If a circle is inscribed in an equilateral triangle, then find the ratio of area of circle to area of triangle?

If a circle is inscribed in an equilateral triangle, then find the ratio of area of circle to area of triangle? Correct Answer π : 3√3

Formula:

Area of equilateral triangle = × a2

Area of circle = πr2

Radius of in-circle = a/2√3

Calculation:

Radius of in-circle for equilateral triangle = a/2√3

Area of circle = π × 2 = π ×

Area of triangle = × a2

Required ratio = π × : × a2

= π : 3√3

∴ The ratio of the area of circle to the area of triangle = π : 3√3

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