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Area of a Sector

Sector Area Formula

There are two sector area formulas; one for a sector measured in radians, and another for a sector measured in degrees. They are given as:

Radians: A = 12θr2
Degrees: A = 1360θπr2

Where A is the area, θ is the sector angle, and r is the radius.

area of a sector

Example Problems

Problem 1:
Find the area of a sector with an angle of 90 degrees and a radius of 10.

1.) Plugging the given dimensions into the formula, we get:
A = 1360θπr2
A = 1360(90)π(102) = 25π
2.) The area is 25π.

Problem 2:
The sector from problem 1 is changed so that the diameter is 10 instead of the radius being 10. What is the new area?

1.) First, let’s convert diameter to radius.
2r = d
2r = 10
r = 5
2.) Now let’s plug the radius and angle into the formula.
A = 1360θπr2
A = 1360(90)π(52) = 6.25π
3.) The area is now 6.25π.

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