Question

What is the area of an equilateral triangle inscribed in a circle of radius $4cm$?

• A. $12{cm}^2$
• B. $9\sqrt{3}{cm}^2$
• C. $8\sqrt{3}{cm}^2$
• D. $12\sqrt{3}{cm}^2$

Answer 1

The correct option is D $12\sqrt{3}{cm}^2$

We have,

Radius of given circle is $=4cm.$

We know that,

The side of equilateral triangle is

$r=\frac{s}{\sqrt{3}}$

$4=\frac{s}{\sqrt{3}}$

$s=4\sqrt{3}cm.$

Now,

Area of equilateral triangle is

$=\frac{\sqrt{3}}{4}\times s^2$

$=\frac{\sqrt{3}}{4}\times 4\sqrt{3}\times 4\sqrt{3}$

$=12\sqrt{3}c{m}^2$

Hence, this is the answer.