The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm.

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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

$=\left(\frac{1}{2} 5.6 \times 16\right) \mathrm{cm}^{2}$

 

$=44.8 \mathrm{~cm}^{2}$

 

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