The radius of a circle inscribed in a regular triangle is equal to the root of 3 cm. Find the perimeter

The radius of a circle inscribed in a regular triangle is equal to the root of 3 cm. Find the perimeter and the area of the triangle.

Since the ABC triangle is equilateral, the radius of the inscribed circle will be equal to:

R = √3 * a / 6, where a is the side of an equilateral triangle.

Then AC = 6 * R / √3 = 6 * √3 / √3 = 6 cm.

Ravs = 3 * AC = 3 * 6 = 18 cm.

In an equilateral triangle, the internal angles are 60, then Sавс = а2 * Sin60 / 2 = 36 * √3 / 4 = 9 * √3 cm2.

Answer: The perimeter of the triangle is 18 cm, the area is 9 * √3 cm2.