Find the area of a circle inscribed in a regular triangle with a side of 6 cm.

A regular triangle is a triangle in which all sides are equal, and all angles are equal, their degree measure is 60 degrees. Let a triangle ABC be given by condition, then AB = BC = AC = 6 cm.
The area of a circle of radius R is found by the formula:
S = πR ^ 2.
The radius of a circle inscribed in a regular triangle is found by the formula:
R = √3a / 6,
where a is the side length of a regular triangle.
Then:
R = √3 * 6/6 = √3 (cm).
Let’s find the area of a circle inscribed in a regular triangle ABC:
S = π * (√3) ^ 2 = 3π (cm ^ 2).
Answer: S = 3π cm ^ 2.