Geometry

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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 = ^{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.

### Example Problems

**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}⁄_{360}θπr^{2}

A = ^{1}⁄_{360}(90)π(10^{2}) = 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?

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}⁄_{360}θπr^{2}

A = ^{1}⁄_{360}(90)π(5^{2}) = 6.25π

3.) **The area is now 6.25π.**