The area of circumscribing circular region of an equilateral triangle is 462 sq. cm. Let us write by calculating length of each side of this triangle.

Given: Area of the circumscribing circular region = 462 cm²

Circle is centered at A.

∵ Area of a circle = πr²

⇒ r = 7√3

So, the radius of the circum circle of this triangle = 7√3 cm.

The centroid of equilateral triangle is at A and lies on height BE.

⇒ BE = 10.5√3 cm

Height of equilateral triangle = 10.5√3 cm

Height of equilateral triangle

⇒ Side of the triangle = 21 cm