Question

figure, A ABC is right angled at A. Semicircles are drawn on AB, BC and AC as diameters. It is given that AB 3cm and ACE 4cm Find the area of the shaded region 4cm ​

Answer 1

In △ABC, ∠A=90°

By Pythagoras theorem,

BC²= AB²+AC²

BC²= 3²+4²

9+16 =25

∴BC= 5cm

Ar(shaded region) =

Ar(△ ABC) + Ar(semicircle AB) + Ar(semicircle AC) - Ar(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 + 9π/8 + 2π − 25π/8

= 6 + 2π − 2π

= 6cm²

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