Question

$\Delta ABC$ is an equilateral $\Delta$ with area $36\sqrt{3}c{m}^2$ The area of the inscribed circle is

• A. $12\pi c{m}^2$
• B. $48\pi c{m}^2$
• C. $24\pi c{m}^2$
• D. $36\pi c{m}^2$

Answer 1

The correct option is A $12\pi c{m}^2$

$Sid{e}^2\times \frac{\sqrt{3}}{4}=36\sqrt{2}$
$\Rightarrow$ Side =12cm
Semi perimeter $=\frac{12\times 3}{2}=18cm$
Radius of the circle $=\frac{36\sqrt{3}}{18}=2\sqrt{3}cm$
Area$=\pi x{\left(2\sqrt{3}\right)}^2=12\pi c{m}^2$