## Area of a Sector Lesson

### 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 =**^{1}⁄_{2}θr^{2}**Degrees: A =**^{1}⁄_{360}θπr^{2}

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

INTRODUCING

### 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:

- Plugging the given dimensions into the formula, we get:

A =^{1}⁄_{360}θπr^{2}

A =^{1}⁄_{360}(90)π(10^{2}) = 25π **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:

- First, let's convert diameter to radius.

2r = d

2r = 10

r = 5 - Now let's plug the radius and angle into the formula.

A =^{1}⁄_{360}θπr^{2}

A =^{1}⁄_{360}(90)π(5^{2}) = 6.25π **The area is now 6.25π.**