Question

The perimeter of a certain sector of a circle of radius 5.6 m is 27.2 m. Find the area of the sector.

Answer 1

We know that the area A of a sector of circle of radius r and arc length l is given by

Let OAB is the given sector. Then,

Perimeter of sector OAB = 27.2 m
OA + OB + arc AB = 27.2 m
5.6 + 5.6 + arc AB = 27.2 m
11.2 + arc AB = 27.2 m

arc AB = 16 m

So, l = 16 m

Now substituting the value of r and l in above formula,

$$\begin{gathered} A=\frac{1}{2}\times 16\times 5.6 \\ =44.8m^2 \end{gathered}$$