area of an arc =lenght of arc *radius/2
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The area under the arc is the angular sweep of the arc (angle covered by the arc) divided by 360, multiply by pie times the square of the radius of the arc. If the value of pi is not given, 3.142 can be used as the value.
if you have the diameter or the arc, then you can divide the diameter by two, or you can use the arc to calculate it.
The area of a sector of a circle with radius 12 and arc length 10pi is: 188.5 square units.
The area of a sector in a circle if the radius is 4 cm and the arc has degree 120 is: 16.76 cm2
There is no direct relation between the area of a sector and the length of an arc. You must know the radius (or diameter) or the angle of the sector at the centre.