Question

A school has decided to give scholar's badges to its scholar students and they w
designed as shown in the figure. PQRS is a diameter of a circle of radius 6cm and
lengths PQ R and RS are equal. Find the perimeter of the shaded portion and
area of non-shaded portion.
What is the importance of a Scholar's badge for a students ?​

Answer 1

The perimeter of shades portion = 37.71 cm

Step-by-step explanation:

Given that PQ = QR

and also, QS is diameter of small semi circle

QR = RS

Therefore,  PQ = QR =RS.....(i)

Radius of circular badge = 6 cm

Diameter of circular badge = 2(6) = 12 cm

From (i) Equation

PS = PQ + +QR + RS

PS = PQ + PQ + PQ

PS = 3PQ

Then 3 PQ = 12

            PQ = 4 cm

PQ = QR = RS =  4 cm

Therefore,  perimeter of semicircle  = πr

 Perimeter of shaded portion = Perimeter of circular part with diameter PS + perimeter of circular part with diameter QS + perimeter of circular part with PQ

= π(6) + π(4) + π(2)

= π ( 6+4+2)

= π (12)

= 37.71

Therefore, The perimeter of shades portion = 37.71 cm