Question

In the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region.

Answer 1

Radius of semicircle PSR = 10cm/2 = 5cm

$RadiusofsemicirclePAQ=\frac{7}{2}=3.5cm$
$RadiusofsemicircleRTQ=\frac{3}{2}=1.5cm$

Perimeter of shaded region = perimeter of semicircle PSR + perimeter of semicircle RTQ + perimeter of semicircle PAQ

$Andweknowthatperimeterofasemicircle=\pi \times r$

$Requiredperimeter=\pi \times 5+\pi \times 1.5cm+\pi \times 3.5$ cm

= 3.14 (5cm + 1.5cm +3.5 cm) = 3.14 x 10cm = 31.4 cm