Question

A sector of a circle of radius cm has an area of  cm². Express the perimeter of the sector in  terms of and .

Solution

We are given that for the circular sector;

We are required to find expression for perimeter of the circular sector.

Expression for perimeter of a circular sector with radius  and angle  rad is;

Therefore, for the given circular sector;

Hence, we need arc length of circular sector.

Expression for length of a circular arc with radius and angle rad is;

Therefore;

We are not given angle rad. We need to find angle  rad.

Expression for area of a circular sector with radius and angle rad is;

Therefore, for the given case;

Hence;