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a school has decided to give scholars badge to its scholar students and they were designed as shown in the figure. PQRS is a diameter of a circle of radius 10.5 cm. the lengths pq and qr are equal. find the perimeter of the shaded portion and area of non shaded portion.how these types of badges help to improve the performance of the student?

Q. A school has decided to give scholars badge to its scholar students and they were designed as shown in the figure. PQRS is a diameter of a circle of radius 10.5 cm. The lengths PQ and QR are equal. Find the perimeter of the

shaded portion and area of non-shared portion. How these types of badges help to improve the performance of the student?

Please find below the solution to the asked query:

Given : PQ = QR and we can see that QS is also a diameter for small semicircle , So QR = RS , Then

PQ = QR = RS --- ( 1 )

Also given radius of circular badge = 10.5 cm , So diameter of circular badge = PS = 2 ( 10.5 ) = 21 cm

And

PS = PQ + QR + RS , from equation 1 w eget

PS = PQ + PQ + PQ

PS = 3 PQ

3 PQ = 21

PQ = 7 , So

PQ = QR = RS = 7 cm

We know perimeter for semicircle ( By taking only circular part or without adding diameter ) = $\mathrm{\pi}$

*r*

So,

Perimeter of shaded region = Perimeter of circular part with diameter PS ( Radius 10.5cm ) + Perimeter of circular part with diameter QS ( Radius 7 cm )+ Perimeter of circular part with diameter PQ ( Radius 3.5cm )

$\Rightarrow \frac{22}{7}\times 10.5+\frac{22}{7}\times 7+\frac{22}{7}\times 3.5\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow 22\times 1.5+22\times 1+22\times 0.5\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow 33+22+11\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{\Rightarrow}\mathbf{66}\mathbf{}$

Therefore,

**Perimeter of shaded region = 66 cm ( Ans )**

By giving these type of badges will boost the confidence of the students and that will help them to improve their performance .

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