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If you're only given the length of the arc, then you can't. You also need to know

the fraction of the circle that's in the sector. You can figure that out if you know

the angle of the arc, or the radius or diameter of the circle.

-- Diameter of the circle = 2 x (radius of the circle)

-- Circumference of the circle = (pi) x (Diameter of the circle)

-- (length of the arc)/(circumference of the circle) = the fraction of the whole circle that's in the sector

or

-- (degrees in the arc)/360 = the fraction of the whole circle that's in the sector

-- Area of the circle = (pi) x (radius of the circle)2

-- Area of the sector = (Area of the circle) x (fraction of the whole circle that's in the sector)

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โˆ™ 2012-12-04 21:20:10
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Q: How do you work out the area of a sector when given the length of the arc?
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