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Question
In the given figure, ∆ABC is right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3 cm and AC = 4 cm. Find the area of the shaded region.
Solution
In triangle ΔABC, we have:
`BC = sqrt("AB"^2 + "AC"^2)`
`=sqrt(9+16)`
`=sqrt(25)`
= 5 cm
Ar(shaded part) = Ar(ΔABC) + Ar(semicircle APB) + Ar(semicircle AQC) - Ar(semicircle BAC)
`= (1/2xx3xx4)+(1/2pixx1.5xx1.5)+(1/2pixx2xx2)-(1/2pixx2.5xx2.5)`
`= {6 + 1/2pi(4+9/4-25/4)}`
= 6 + 0
= 6 cm2
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