The perimeter of a regular triangle is 12. Find the area of a circle inscribed in a given triangle.

1. Find the side length of a regular triangle if the perimeter of a triangle with all sides equal is 12 cm:

12/3 = 4 cm, one side;

2. Find the radius of the circle that is inscribed in this isosceles triangle by the formula:

R = √3 / 6 * a;

R = √3 / 6 * 4 = √3 * 2/3 = 2 / √3 cm;

3. Find the area of a circle inscribed in an isosceles triangle by the formula:

S = nR²;

S = 3.14 * (2 / √3) ² = 3.14 * 4/3 = 12.56 / 3 = 1256/300 = 4 56/300 = 4 14/75 cm²;

Answer: the area of a circle inscribed in a triangle 4 is 14/75 cm².