The perimeter of a sector of radius 5.2 cm is 16.4 cm, the . . .

Question : The perimeter of a sector of radius 5.2 cm is 16.4 cm, the area of the sector is 

a) 31.2 cm²
b) 15 cm²
c) 15.6 cm²
d) 16.6 cm²

Doubt by Gauri

Solution :

r = 5.2 cm

Perimeter of the Sector (P) = 16.4 cm

P = (θ/360°)×2πr + 2r

16.4 = [(θ/360°)×π + 1]×2r
16.4 = [(θ/360°)×π + 1]×2(5.2)
16.4 = [(θ/360°)×π + 1]×10.4
16.4/10.4 = (θ/360°)×π + 1
164/104 = θπ/360° - 1
(41/26) - 1 = θπ/360°
(41-26)/26 = θπ/360°
15/26 = θπ/360°

θπ/360° = 15/26 — (1)

Area of sector 

= (θ/360°)×πr²
= (15/26)×(5.2)²
= (15/26)×(52/10)²
= (15×52×52)/(26×10×10)
= (15×2×52)/100
= (30×52)/100
= 1560/100
= 15.6 cm²

Hence, c) would be the correct answer.