Question

In Fig, PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region. [Use π = 3.14]

Answer 1

Radius of semicircle PSR = 10cm/2 = 5cm
Radius of semicircle PAQ = 7cm/2 = 3.5cm
Radius of semicircle RTQ = 3cm/2 = 1.5cm

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

And we know that perimeter of a semicircle = $\pi * r$

Required perimeter = [tex] \pi * 5 cm + \pi *1.5 cm + \pi * 3.5 cm [/tex]

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

Answer 2

Radius = 1/2 × Diameter

Radius of semicircle PSR = 1/2 × 10 = 5 cm
Radius of semicircle RTQ = 1/2 × 3 = 1.5 cm
Radius of semicircle PAQ = 1/2 × 7 = 3.5 cm

Perimeter of the shaded region = (Circumference of semicircle PSR) + (Circumference of semicircle RTQ) - (Circumference of semicircle PAQ)

= [1/2× 2π(5)] + [1/2× 2π(1.5)] – [1/2× 2π(3.5)] 

= π (5 + 1.5 - 3.5) 

= 3.14 × 3 

= 9.42 cm