Find the area of the shaded region, Mathematics

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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 =90⁰

BC = 10cm; AB = 6cm;
∴ AC = 6cm

Area of the Δ =1/2 x 6 x 8= 24 cm²

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 = 24

1/2 r [10 + 8 + 6] = 24

r= 2 cm

∴ Area of circle = Π r² = 22/7 x 2 x 2 = 88/7 cm²

Area of shaded region = 24 - 88/7 = 168 - 88/7 = 80/7 cm²

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