In the given figure, ABC is a right angled at A . semicircles are drawn on AB, AC and BC as diameters. find the area of shaded region.
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IN ΔABC, ∠A=90°
BY PYTHAGORAS THREOM,
BC² = AB² + AC²
BC² = 3² + 4²
BC² = 9 + 16
BC² = 25
BC² = 5²
BC = 5
A(shaded region)=A(△ ABC)+A (semicircle AB) + (semicircle AC) - A(semicircle BAC)
= 1/2 × 3 × 4 + 1/2 × π (3/2)² + 1/2 × π (4/2)² + 1/2 × π (5/2)²
= 6 + 6π/8 +2π -25π /8
= 6 + 2π -2π
= 6 cm²
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