Question

what is the ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal

Answer 1

Let the diameter and side of equilateral triangle be r

Then radius = r/2

Area of Circle,

A1 = π(r/2)² = πr²/4 ......(1)

Now,

Side of equilateral triangle = r

Area of equilateral triangle

A2 = (√3/4)r² = √3 r²/4 .....(2)

Dividing eq(1) by eq(2)

We get,

A1/A2 = π/√3

or A1:A2 = π:√3