Question

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 $\pi =3.14$]

Answer 1

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

Perimeter of the shaded region
= Circumference of semicircle PSR + Circumference of semicircle PAQ
= $\frac{1}{2}\times 2\times \pi \times 5+\frac{1}{2}\times 2\pi \times 1.5+\frac{1}{2}\times 2\pi \times 3.5$
= $\pi (5+1.5+3.5)$
= 3.14 × 10
= 31.4 cm

Therefore, the perimeter of the shaded region is 31.4 cm.