**Q) The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.**

**Ans: **

Given that the radius = 5.6 m

In a circle, perimeter of the sector is given by, P = 2 r + L

Here, L is the arch length of a sector

We are given the values: P = 20 m, r = 5.6 m,

∴ 20 = 2 x 5.6 + L

∴ L = 20 – 11.2 = 8.8 m

Next, we need to find area of the sector

and area of circle’s sector is given by, A = r L *(check derivation below)*

By substituting values of r and L, we get:

A = x (5.6) (8.8)

= 5.6 x 4.4 = 24.64 m^{2 }

**Th erefore, The area of the sector is 14 m^{2}**

**[ Derivation: **

*Length of the arch is given by, L = 2 π r*

*hence ……………. equation (i)*

*Next, Area of the circle’s sector is given by, A = π r ^{2 }*

*∴ A = r (π r ) *

*By substituting values of L from equation (i), we get:*

*A = r ( L)*

*∴* *A = r L ***]**

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