The area of an equilateral triangle inscribed in a circle of radius 2 unit is:

Correct option is C

Given:

An equilateral triangle is inscribed in a circle.

The radius of the circle is 2 units.

Formula Used:

Relationship between the radius of a circumscribed circle and the side of an equilateral triangle: radius (R) = $$\frac{a\text{(side)}}{\sqrt{3}}$$​​

Area of an equilateral triangle: Area = $$\frac{\sqrt{3} }{ 4} \times (side)^2$$​​

Solution:

Find the side of the equilateral triangle:

We know R = 2.

Therefore, 2 = $$\frac{a }{\sqrt{3}}$$​.

$$a=2\sqrt{3}$$​

$$Area=\frac{\sqrt{3} }{ 4} \times (2\sqrt3)^2$$​

Area =  $$\frac{\sqrt{3} }{ 4} \times$$​12

Area = 3$$\sqrt 3$$​​

Therefore, the area of the equilateral triangle inscribed in a circle of radius 2 units is 3$$\sqrt 3$$​ square units.