How Do You Find the Area of a Sector of a Circle?

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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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.