text: # The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm.
  
  Question:
  
  The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.
  
  Solution:
  
  Let O be the centre of the circle with radius 5.6 cm and OACB be its sector with perimeter 27.2 cm.
  Thus, we have:
  
  $O A+O B+\operatorname{arc} A B=27.2$
  
  $\Rightarrow 5.6+5.6+\operatorname{arc} A B=27.2$
  
  $\Rightarrow \operatorname{arc} A B=16 \mathrm{~cm}$
  
  Now,
  
  Area of the sector $O A C B O=\left(\frac{1}{2} \times\right.$ Radius $\left.\times l\right)$ square units
  
  $=\left(\frac{1}{2} 5.6 \times 16\right) \mathrm{cm}^{2}$
  
  $=44.8 \mathrm{~cm}^{2}$