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# Area of a sector?

How do I find the area of a sector when given angle of 30 degrees and length of arc as 6 pi?

### 2 Answers

- 1 decade agoFavorite Answer
30/360 = 1/12 of a complete circle.

If the arc is 6pi, the circumference is 12 * 6 pi = 72 pi.

divide by pi to get the diameter: 72.

The radius is half that, or 36.

The area of the complete circle is pi * 36^2, or 1296 pi. The area of the sector is 1/12th of that.

1296pi / 12 = 108 pi

But you'll need to tack on the units to that answer.

108 pi square meters?

108 pi square inches?

- Stephan BLv 51 decade ago
If you have the angle, and the length of the arc, you can work out the radius (hint, convert the angle into radians, then see http://en.wikipedia.org/w/index.php?title=Arc_%28g... )

As you then have the radius, and the fraction of a circle represented by 30degrees, you can then work out the area of the sector