The length of a circle circumscribed about a regular triangle is 4п cm. Find the area of this triangle.

Knowing the length of the circumscribed circle, we determine its radius.

C = 2 * π * R.

R = C / 2 * π = 4 * π / 2 * π = 2 cm.

Since the ABC triangle is correct, the radius of the circle described around it is equal to:

R = a / √3, where a is the length of the side of the triangle.

AC = AB = BC = R * √3 = 2 * √3 cm.

In a regular triangle, all internal angles are 60, then Savs = AB * BC * Sin60 / 2 =

2 * √3 * 2 * √3 * √3 / 4 = 3 * √3 cm2.

Answer: The area of the triangle is 3 * √3 cm2.