Question

In the the following 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

Answer:

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

HOPE THIS ANSWER WILL HELP YOU….

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Answer 2

I found that most of the students are confused about the perimeter/circumference of semicircle. The length of the curved path of a semicircle is it's perimeter.. We should not add the diameter..

Radius of PR= $\frac{10}{2}$ = 5cm

Radius of PQ= $\frac{7}{2}$ = 3.5cm

Radius of QR= $\frac{3}{2}$ = 1.5cm

Perimeter of PSR= πR

= 3.14 × 5

= 15.7cm

Perimeter of PAQ= πR

= 3.14 × 3.5

= 10.99cm

Perimeter of RTQ= πR

= 3.14 × 1.5

= 4.71cm

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

= 15.7cm + 10.99cm + 4.71cm

= $\fbox{ 31.4 cm }$