What is the area of a sector of a circle that has a diameter of 10 in. if the length of the arc is 10 in?
1 Answer
Explanation:
If a circle has radius

Its circumference is
#2pi r# 
Its area is
#pi r^2#
An arc of length
So the area of a sector formed by such an arc and two radii will be
#1/(2pi) xx pi r^2 = r^2/2#
In our example, the area of the sector is:
#(10"in")^2/2 = (100"in"^2) / 2 = 50"in"^2#
"Paper and Scissors" Method
Given such a sector, you could cut it up into an even number of sectors of equal size, then rearrange them head to tail to form a slightly "bumpy" parallelogram. The more sectors you cut it into, the closer the parallelogram would be to a rectangle with sides
I don't have a picture for that, but here's an animation I put together that shows a similar process with a whole circle, illustrating that the area of a circle (which has circumference