Question

A circle has a radius of 6 in. The inscribed equilateral triangle will have an area of:

Answer 1

Area of circle =TTr ^2
=22 /7*6*6
115. 14

Answer 2

Answer:

The area of the inscribed equilateral triangle is $27\sqrt3$

Step-by-step explanation:

Let the equilateral triangle ABC is inscribed in a circle of radius 6 and centered at O.

In right triangle, we have

$\cos30=\frac{a/2}{6}\\\\\frac{\sqrt3}{2}=\frac{a}{12}\\\\a=6\sqrt3$

Therefore, the area of the equilateral triangle is given by

$A=\frac{\sqrt3}{4}a^2\\\\A=\frac{\sqrt3}{4}(6\sqrt3)^2\\\\\A=27\sqrt3$

The area of the inscribed equilateral triangle is $27\sqrt3$