Question

In equilateral triangle, each side has $6cm$ then the area of incircle = _____$c{m}^2$

• A. 3$\pi$
• B. $9\pi$
• C. $12\pi$
• D. $36\pi$

Answer 1

Answer: (A)

3$\pi$

Given Side of equilateral tringle is $a=6cm$

$\Delta =\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}\times 6^2=9\sqrt{3}c{m}^2$

$s=\frac{3a}{2}=\frac{3\times 6}{2}=9cm$

$r=\frac{\Delta }{s}=\frac{9\sqrt{3}}{9}=\sqrt{3}cm$

Area of incircle is $\pi r^2=\pi (\sqrt{3}{)}^2=3\pi c{m}^2$