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

Radius of circle $r=\frac{d}{2}$

And side of triangle $a=d$

Ratio$=\frac{areaofthecircle}{areaofthetriangle}=\frac{\pi r^2}{\frac{\sqrt{3}}{4}{a}^2}$

$=\frac{\frac{\pi d^2}{4}}{\frac{\sqrt{3}}{4}{d}^2}$

$=\frac{\pi }{\sqrt{3}}$