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How to Calculate the Area of a Segment

Circle geometry is a common type of math problem. The radius of a circle is the distance from the center to any point located on the circle. A sector is a fraction of the circle bounded by two radii; a common example of a sector is a pizza slice. The angle between the radii determines the area of the sector. Calculate the sector area using the circle radius and the mathematical constant "pi."

Things You'll Need

Calculator

Instructions

- 1
  Obtain the constant "pi" with the required precision (see References). The pi value rounded to thousands (3.142) is typically sufficient.
- 2
  Divide the sector angle by 360, and then multiply the result by the constant pi. For example, if the sector angle is 30 degrees, then (30 / 360) x 3.142 = 0.262.
- 3
  Raise the radius of the circle to the square. For example, if the radius is 3 inches, then 3 x 3 = 9 square inches.
- 4
  Multiply the values obtained in steps 2 and 3 to calculate the area of the sector. In our example, the sector area is 0.262 x 9 square inches = 2.358 square inches.

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