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How to Calculate the Area of a Sector With Arc Length

A circle can be broken down into sectors, which are formed by two radii and an arc. The arc sector angle measure equals the angle at which the two radii intersect. If you know the arc length and the angle measure, you can calculate the radius of the circle sector. From the radius you can find the area of the sector. You might want to calculate the area of the sector to figure the amount of sod you need to plant or the amount of paint you need to use.

Instructions

    • 1

      Divide the angle measure of the sector by 57.297 to convert the measure to radians. For example, if the sector angle equals 100 degrees, divide 100 by 57.297 to get 1.745 radians.

    • 2

      Divide the sector length by the angle measure in radians to find the radius. In this example, if the arc length equals 9, divide 9 by 1.745 to get 5.16 as the radius.

    • 3

      Square the radius. For this example, multiply 5.16 by 5.16 to get 26.6256.

    • 4

      Multiply the result by the sector angle measure in radians. In this example, multiply 26.6256 by 1.745 to get 46.461672.

    • 5

      Divide the result by 2 to find the area of the sector. In this example, divide 46.461672 by 2 to find the area of the sector equals about 23.23.

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