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

Explanation

From right `DeltaBAC` we get
`BC=sqrt(AB^(2)+AC^(2))=sqrt(3^(2)+4^(2))`
`=sqrt(9+16)=sqrt(25)=5cm`
Area of the shaded region
`={ar(DeltaABC)+ar("semicircle" APB)+ar("semicircle" AQC)}-ar("semicircle"BAC)`
`=[(1/2xx3xx4)+(1/2pixx3/2xx3/2)+(1/2pixx2xx2)-(1/2pixx5/2xx5/2)]cm^(2)`
`={6+1/2pi(9/4+4/25/4)}cm^(2)=(6+0)cm^(2)=6cm^(2)`
Hence, the area of the shaded region is `6cm^(2)`