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:

1. Radians: A = ¹⁄₂θr²
2. Degrees: A = ¹⁄₃₆₀θπr²

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

Area of a Sector Example Problems

Let's work through a couple of example problems together to practice finding the area of a sector.

Example Problem 1

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

Solution:

1. Plugging the given dimensions into the formula, we get:
   A = ¹⁄₃₆₀θπr²
   A = ¹⁄₃₆₀(90)π(10²) = 25π
2. The area is 25π.

Example 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?

Solution:

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 = ¹⁄₃₆₀θπr²
   A = ¹⁄₃₆₀(90)π(5²) = 6.25π
3. The area is now 6.25π.