This math skill describes calculating the area of a sector of a circle given the arc length. First, find the circle's circumference to determine the fraction of the circle the arc covers. Then, use this fraction to find the sector area by applying it to the circle’s total area.
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Area of a sector of a circle from arc length
Test your understanding of area of circle sector from arc by practicing it! Work through the below exercises to use it in practice.
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What is the area of the sector of this circle with an arc length of 4 Pi?
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The circle has a radius of 6, so we can calculate the circumference of the full circle with 2 pi times the radius. We have a circumference of 12 Pi
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Since our arc has a length of 4 Pi, and the total circumference is 12 Pi, our arc covers one third of the circumference, and therefore the sector is one third of the total area
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The circle has a radius of 6, so we can calculate the area of the full circle with pi times the radius squared, That would be a full area of 36 pi
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But we only have one third of the circle, so we need to multiply by one third, so our sector area is 12 pi.
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If we want to have it as a decimal, we can use 3.14 for pi, and it would be approximately 37.7