How to Calculate the Chord Area

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A chord is a line that travels from one point to another on a circle's circumference while bisecting the circle's area. The area that is contained between the chord and the circumference is called a segment of the circle and is part of a greater area called a sector. Calculation of the segment area can be accomplished using the radius of the circle and the angle of the chord's sector, also called the central angle. Learning to calculate the area affected by the chord can help your understanding of the individual parts of a circle.

Things You'll Need

  • Scientific calculator
  • Multiply the central angle by π and then divide that product by 180. For example, the central angle is 120, and multiplying that by π equals 376.991. Dividing that number by 180 results in 2.094.

  • Calculate the sine function of the central angle and then subtract the sine amount from the previous amount. For the example, the sine of 120 is 0.866. Subtracting that from 2.094 results in 1.228.

  • Multiply that amount by the radius squared. For the example, the radius is 8, so squaring the radius results in 64. Multiplying 64 by 1.228 results in 78.616.

  • Divide that number by 2. For the example, 78.616 divided by 2 equals 39.308, which is the area of the circle separated by the chord.

References

  • Photo Credit Hemera Technologies/AbleStock.com/Getty Images
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