ABC is a right angled triangle in which ∠A = 900. Find the area of the shaded region if AB = 6 cm, BC=10cm & I is the centre of the Incircle of ?ABC.
Ans: ∠A =90^{0}
BC = 10cm; AB = 6cm;∴ AC = 6cm Area of the Δ =1/2 x 6 x 8= 24 cm^{2}
Let the Radius of the Incircle be r
∴ 1/2 x 10 x r + 1/2 x 8 x r +1/2 x 6 x r = 241/2 r [10 + 8 + 6] = 24
r= 2 cm
∴ Area of circle = Π r^{2} = 22/7 x 2 x 2 = 88/7 cm^{2}
Area of shaded region = 24 - 88/7 = 168 - 88/7 = 80/7 cm^{2}