Question

The perimeter of a certain sector of a circle of radius 6.5 cm in 31 cm. Find the area of the sector.

Answer 1

Given:
Radius = 6.5 cm


Let O be the centre of the circle with radius 6.5 cm and OACBO be its sector with perimeter 31 cm.
Thus, we have:
OA + OB + arc AB = 31 cm

$$\begin{gathered} \Rightarrow 6.5+6.5+arcAB=31 \\ \Rightarrow arcAB=31-13 \\ \Rightarrow arcAB=18\mathrm{cm} \end{gathered}$$

Now,
Area of the sector OACBO = $\frac{1}{2}\times \mathrm{Radius}\times \mathrm{Arc}$
$$\begin{gathered} =\frac{1}{2}\times 6.5\times 18 \\ =58.5{\mathrm{cm}}^2 \end{gathered}$$
​