Question

In the given figure, $PQR$ is a right-angled triangle right-angled at $P$. Semicircles are drawn with $PQ,PR$ and $QR$ as diameters. If $PQ=6cm$, $QR=10cm$ and $PR=8cm$, find the area of the shaded region.

Answer 1

Area of circle with $QR$ as diameter $=\frac{\pi \left(5^2\right)}{2}=\frac{25\pi }{2}c{m}^2$

Area of semi circle with diameter $PR$

$=\frac{\pi \left(4^2\right)}{2}=8\pi c{m}^2$

Area of semi circle with $PQ$ diameter

$=\frac{\pi \left(3^2\right)}{2}=\frac{9\pi }{2}c{m}^2$

Area of triangle $PQR=\frac{1}{2}\times 6\times 8=24c{m}^2$

Area of shaded regions

$=(8\pi +\frac{9\pi }{2}+24)-\left(\frac{25\pi }{2}\right)=12.5\pi +24-12.5\pi =24c{m}^2$