In figure 2, ABC is a right-angled triangle at A. Semi-circles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.
Given: ABC is a right triangle with ∠A = 90°
and AB = 6cm and AC = 8cm
To find: Area of Shaded region
Proof: In ΔABC, Using Pythagoras Theorem
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
(BC)2 = (8)2 + (6)2
⇒ (BC)2 = 64 + 36
⇒ (BC)2 = 100
⇒ BC = √100
⇒ BC = 10
∴ BC = 10cm
= 24 cm2
Area of shaded Region
= Ar of semicircle with radius 3 + Ar of semicircle with radius 4 – [Ar of semicircle with radius 5 – Area of ΔABC]
= 24cm2
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