We can solve this question in 2 ways: either using
degrees or converting the degrees into
radians.
Since, the question says degrees itself and there is no specification of using radians only, so I have solved it using degrees itself.
Part (a):
Perimeter of sector ORS = 2*Radius + Arc RS = 2*21 +

Part (b):
Area of sector ORS =

Area of sector POQ =

Thus, area of shaded region
= Area of sector ORS - Area of sector POQ
=
Solution:
<u>Simplify the equation and solve for r.</u>
- r/16 + 6 = 7
- => r/16 = 7 - 6
- => r/16 = 1
- => r = 16
The value of r is 16.
<u>Check:</u>
- r/16 + 6 = 7
- => 16/16 + 6 = 7
- => 1 + 6 = 7
- => 7 = 7 (Proved correct)
Do you have a picture you can upload? It’s most likely 24/2 = 12