Question

A circle is inscribed in an equilateral triangle touching all the three sides. If the radius of the circle is 2 cm then find out the area of triangle acio ib

Answer 1

Observe the attached figure, and we see that the angle is 30°, because it is an equilateral triangle.

tan 30° = OD/AD = 2/AD = 1/√3 (∵ standard t-ratio)

AD = 2√3, and therefore, side AB = 2*2√3 = 4√3 cm

Area of an equilateral triangle = (√3/4)*side²

Area = √3/4 * (4√3)²

= √3/4 * 48 = 12√3 cm²