A circle of radius r is inscribed in a regular triangle. find the area of a triangle

univerkov | April 29, 2021 | education

Since the triangle is regular, the radius of the inscribed circle is:

R = AC * √3 / 6, then AC = 6 * R / √3 = 2 * R * √3 cm.

Since the triangle is regular, its area is:

Str = AC ^ 2 * Sin60 / 2 = 4 * R ^ 2 * 3 * √3 / 4 = 3 * R ^ 2 * √3 cm2.

Answer: The area of the triangle is 3 * R ^ 2 * √3 cm2.

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