A circle has a radius of 6 cm. What would be the area of an inscribed equilateral triangle?

Solution:

Given, the circle has a radius = 6 cm.

An equilateral triangle is inscribed in a circle.

For an equilateral triangle all sides are equal and angle is equal to 60°.

To find the area of an equilateral triangle inscribed in a circle, we have to find the length of the side of the equilateral triangle.

The side of the equilateral triangle is r = side / √3

⇒ Side = r × √3

⇒ Side = 6 × √3

⇒ Side = 6√3 inches

Now the area of the equilateral triangle is √3 / 4 × (side)²

⇒ Area = √3 / 4 × 6√3 × 6√3

⇒ Area = 27√3 cm²

Therefore, the area of an inscribed equilateral triangle is 27√3 cm².

A circle has a radius of 6 cm. What would be the area of an inscribed equilateral triangle?

Summary:

If a circle has a radius of 6 cm then the area of an inscribed equilateral triangle is 27√3 cm².