Question

In the figure PSR, RTQ and PAQ are 3 semicircles of diameters 10cm, 3cm and 7cm respectively. Find the area of shaded region.​

Answer 1

Step-by-step explanation:

The perimeter of the shaded region is 31.4 cm

Step-by-step explanation:

Given :

Diameter of semicircle PSR = 10 cm

Diameter of semicircle RTQ = 3 cm

Diameter of semicircle PAQ = 7 cm

Radius of semicircle PSR , r1 = 10/2 = 5 cm

Radius of semicircle RTQ, r2 = 3 cm = 3/2 cm

Radius of semicircle PAQ, r3 = 7/2 cm

Perimeter of the shaded region = Length of the arc PAQ + Length of the arc PSR + Length of the arc RTQ

= πr1 + πr2 + πr3

= π(r1 + r2 + r3)

= π(5 + 3/2 + 7/2)

= π{(10 + 3 + 7)/2}

= π × 20/2

= 10 π

= 10 × 22/7

= 10 × 3.14

= 31.4 cm

Perimeter of the shaded region = 31.4 cm

Hence, the perimeter of the shaded region is 31.4 cm

Answer 2

Step-by-step explanation:

$\frac{1}{2} (\pi( {10}^{2} - {7}^{2} + {3}^{2} )) \\ \frac{1}{2} (\pi(100 - 49 + 9)) \\ 30\pi$