Question

Find the area of a circle circumscribing an equilateral triangle of wide 15 cm.​

Answer 1

Let the radius of the circle be r , this circle also circumscribing the equilateral triangle of side a = 15 cm

so from the relation between radius and side of triangle we get

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Answer 2

$\huge\rm\underline\pink{Solution:-}$

Radius of circle when it circumscribes an equilateral triangle of side 'a' is a/√3

Given side of equilateral triangle = 15 cm

$\large\rm{\implies{Radius\:of\:circle\:=\:\frac{15}{\sqrt{3}}}}$

$\large\rm\bold{\boxed{Area\:of\:circle\:=\:πr^2}}$

$\large\rm{Area\:of\:circle\:=\:3.14\times(\frac{15}{\sqrt{3}})^2}$

∴ Area of circle = 235.4 cm²