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 + [tex]60* \frac{ \pi }{180} *21 = \frac{ \pi }{3} *21 = 7 \pi [/tex]
Part (b):
Area of sector ORS = [tex] \frac{60}{360} * \pi * 21^{2} = \frac{1}{6} * \pi *21*21= \frac{147}{2} \pi [/tex]
Area of sector POQ = [tex] \frac{36}{360} * \pi * 14^{2} = \frac{1}{10} * \pi * 196 = \frac{196}{10} \pi [/tex]
Thus, area of shaded region
= Area of sector ORS - Area of sector POQ
= [tex]\frac{147}{2} \pi - \frac{196}{10} \pi = \frac{735 - 196}{10} \pi = \frac{539}{10} \pi = 53.9 \pi [/tex]
