In Fig 4, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region.[Use π=3.14 and √3=1.73]
It is given that ABC is an equilateral triangle of side 12 cm.
Join OA, OB and OC.
Let the radius of the circle be r cm.
Area of ∆AOB + Area of ∆BOC + Area of ∆AOC = Area of ∆ABC
Therefore, the radius of the inscribed circle is 3.46 cm.
Now, area of the shaded region = Area of ∆ABC − Area of the inscribed circle
Therefore, the area of the shaded region is 24.6 cm2