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.

Answer 1

$BC=\sqrt{(3^2+4^2)}=5cm$

Area of shaded region = Total Area of the figure - area of unshaded region

=Area of triangle ABC + Area of semi-circle with AB as diameter + Area of semi-circle with AC as diameter - Area of semi-circle with BC as diameter

=$(0.5\times 3\times 4)+(\pi \times \times 3^2)+(\pi \times \times 4^2)-(\pi \times \times 5^2)=6+9\pi +16\pi -25\pi =6c{m}^2$