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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)

Q: How do you work out the area of a sector when given the length of the arc?

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Not enough information is given to work out the radius of the circle as for instance what is the length of sector's arc in degrees

The area sector of a circle needs pi to work it out.

That's really going to depend on the angle of the sector. Even just knowing the length of the arc would help a lot. Give us something to work with. Anything !

Yes. That is often how pie charts work.

1. The segment will be enclosed within a sector of radii 18 cm and an arc angle of about 113 degrees. 2. Area of sector: 113/360*pi*18*18 = 319 square cm rounded. 3. Area of segment: 316-area of isosceles triangle contained in the sector = 170 square cm rounded.

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Not enough information is given to work out the radius of the circle as for instance what is the length of sector's arc in degrees

The area sector of a circle needs pi to work it out.

The way you can work out the length of a triangle is if you are given the height and the area of that triangle ( this works of you don't want to measure it) or you could just measure it.

That's really going to depend on the angle of the sector. Even just knowing the length of the arc would help a lot. Give us something to work with. Anything !

Yes. That is often how pie charts work.

1. The segment will be enclosed within a sector of radii 18 cm and an arc angle of about 113 degrees. 2. Area of sector: 113/360*pi*18*18 = 319 square cm rounded. 3. Area of segment: 316-area of isosceles triangle contained in the sector = 170 square cm rounded.

the area of a sector = (angle)/360 x PI x radius x radius pi r squared

You just multipy the length (no matter what it is) by the width (no matter what that is). So... L x W = A Where L is Length, W is Width and A is Area. For your question about the area of a rectangle where the length is twice the width but no numbers are given then I guess a formula could be W x 2W = A. Or send me the exact question and I'll see if I can think of a better answer.

You times length by width

Knowing just the length of the base you can not work out the area. You need the height and the base or the length of the hypotenuse in order to work out the area.

That is the definition of the area of a rectangle. It does not work for any other shape.