what is the area enclosed by a circular sector whose radius r and arc length is s?

Question

Can someone please help me get the answer to this question please.

Answer 1

The sector area is proportional to the arc length.

• Let the (r) equal the radius of the circle.
• Let (s) equal the arc length.

The area of the enclosed sector is given by:

 

                      A_sector = (r*s)/2

 

You can arrive at this answer by understanding the that the ratio of the sector length (s) and the circle's circumference (C) = 2*¶*r times the area of the circle (A) = ¶*r^2. Set this up as follows:

 

                        A_sector = (s/2*¶*r)*(¶*r^2) strike through like terms cancel.

                        A_{sector = (s*r)/2}