Question

What is the ratio of the area of a circle and an equilateral triangle whose diameter and a side?

Answer 1

Answer:

Area of circle --

$\pi {r}^{2}$

area of equilateral triangle--

$\frac{ \sqrt{4} }{3} {a}^{2}$

so that ,

Answer 2

Let diameter of a circle = Side of an equilateral ∆ = 2a

$\therefore$$\sf\red{ \frac{area \: of \: a \: circle}{area \: of \: equilateral∆} = \frac{ {\pi \: a}^{2} }{ \frac{ \sqrt{3} }{4} \times {(side})^{2}}}$

$\longrightarrow$$\sf\red{\frac{ {\pi \: a}^{2} }{ \frac{ \sqrt{3} }{4} \times ( {2a)}^{2} } = \frac{ {\pi \: a}^{2} }{ \frac{ \sqrt{3} }{4} \times {4a}^{2} } = \frac{\pi}{ \sqrt{3} } = π:\sqrt{3} }$