Question

In an equilateral triangle of side 24 cam circle is inscribed touching its sides.find the area of the remaining portion of the triangle

Answer 1

Area of equilateral triangle ABC with side 24 cm = √3/4 x a2 = √3/4 x 242 = 144 √3 cm2 ----------------------(1) Let r be the radius of the inscribed circle. Then Area of triangle ABC = Area of triangle OBC + Area of triangle OCA + area of triangle OAB = 1/2 x r x BC + 1/2 x r CA + 1/2 x r x AB = 1/2 x r x (BC + CA + AB) = 1/2 x r x (24 + 24 + 24) = 1/2 x r x 72 = 36 r cm2 ------------------------------------------------------------------------ (2) From (1) and (2), we get 36r = 144 √3 Implies, r = 4 √3 Therefore, Area of the inscribed circle = Π r2 = 22/7 x (4 √3)2 = 150.85 cm2 Therefore, Area of the remaining portion of the triangle = area of triangle ABC – area of inscribed circle = 144 √3 – 150.85 = 144 x 1.73 – 150.85 = 249.408 – 150.85 = 98.551 cm2