Question

PQRS is a diameter of a circle of radius 6cm. the lengths PQ , QR , and RS are equal .Semicircles are drawn on PQ and QS as diameters. Find the perimeter of the shaded region ??

Answer 1

$r=6 \\d=2r=12 \\PQ=QR=RS= \frac{d}{3} = \frac{12}{3} =4 \\ \\P= \frac{1}{2}\times 2r\pi+\frac{1}{2}\times 2\times QR\times\pi+\frac{1}{2}\times 2 \frac{PQ}{2} \pi \\ \\P=r\pi+QR\times\pi+\frac{PQ}{2} \pi \\ \\P=6\pi+4\pi+\frac{4}{2} \pi \\ \\P=12\pi$