Question

A circle is inscribed in an equilateral triangle ABC of side 12 cm, touching its sides (fig.,). Find the radius of the inscribed circle and the area of the shaded part.

Answer 1

Given,

An equilateral triangle of side = 12 cm

Area of the equilateral triangle = √3/4(side)²

= √3/4(12)² = 36√3 cm²

Perimeter of triangle ABC = 3 x 12 = 36 cm

So,

The radius of incircle = Area of triangle/ 1/2 (perimeter of triangle)

= 36√3/ 1/2 x 36

= 2√3 cm

Therefore,

Area of the shaded part = Area of equilateral triangle – Area of circle

= 36√3 – πr²

= 36(1.732) – (3.14)(2√3)²

= 62.352 – 37.68

= 24.672 cm²