Question

How to find the the area and perimeter of a sector?

Answer 1

A sector is a part of a circle. It is bounded by two radii and an arc.
The arc is a fraction of the circle proportional to its central angle.

Area of circle = (pi)r^2
Central angle of arc measures k degrees.
Then Area of sector = (k/360)(pi)r^2

The perimeter is the sum of two radii and the length of the arc.
The arc is a portion of the circumference of the circle porportional; to the measure of the cenrtral angle.
Central angle is k degrees
Circumference of circle = 2(pi)r
Length of arc = (k/360)(2)(pi)r = (k/180)2(pi)r
Perimeter = 2r + (k/180)2(pi)r