The equation for the area of a circle is pi times the square of the radius or A = πr2. Calculating the area of a sector involves figuring out what fraction of the circle's area the sector covers.
- Understand A = πr2
The radius of a circle is defined as a line segment drawn from the circle's center to any point on its edge. Pi is the ratio of a circle's circumference to its diameter. Pi is an irrational number, meaning it is a decimal that does not terminate or repeat, but for everyday purposes, it can be rounded to 3.14.
- Apply the circle area formula
Suppose a circle has a radius of 10 centimeters. To find its area, square 10 to get 100, and then multiply by 3.14. The circle's area is 314 square centimeters.
- Figure out units of arc
Recall that the edge of a circle spans 360 degrees. A right angle drawn from the circle's center and intersecting its edge covers 90 degrees of arc. The area of this sector would be 90/360 or 1/4 the area of the whole circle. Other angles work the same way when drawn at the circle's center. This is the remaining step necessary to calculate the area of a sector.
- Try a sample problem
Go back to the circle in step 2. Suppose a 60-degree angle is drawn at the circle's center. The area of the circle is 314, and 314 divided by 6 is 52.33. Therefore, a sector with a central angle of 60 degrees inscribed a circle with a radius of 10 centimeters has an area of 52.33 square centimeters.