Question

perimeter of a sector of a circle of radius 12 cm is 36 cm find area of the sector

Answer 1

u will get theta from first stepand u have to keep the value in formula of area

Answer 2

Answer:

Area of the sector = 66 cm²

Step-by-step explanation:

Given data

Perimeter of a sector = 36 cm

Radius of the  circle = 12 cm

here we need to find area of the sector    

we know that perimeter of a sector = $2r + 2\pi r$(θ/360)  

from given data

        2(12) + 2(22/7)12 (θ/360) = 36 cm  

         $24 + \frac{2(22)(12)}{7(360)}$ θ = 36

         $\frac{44(12)}{7(360)}$ θ = 36 - 24

         θ $=$ $\frac{11(7)(360)}{44(12)}$  

         θ = 52.5°  

area of the sector with angle 52.5°  =  $\frac{x}{360}\pi r^{2}$  

                                                           = $\frac{52.5}{360} (\frac{22}{7} )(12)(12)$  

                                                          =  66 cm²