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: 

We know that the perimeter of a circle’s sector making θ angle, is given by: P = 2 R + 2 π R

∴ π R = ……..(i)

And the area of the circle’s sector making θ angle, is given by: A =  π R ²

by substituting values from equation (i), we get:

A =  π R ²

A =  R x π R   = R x

Here we are given, radius R = 5.6 m, Perimeter P = 20 m

By substituting these values in above formula, we get:

A = R x

∴ A = 5.6 x

∴ A = 5.6 x

∴ A = 5.6 x = 5.6 x 4.4 = 24.64

Therefore, the area of the sector is 24.64 m²

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