NOTE: If you need to refresh your memory regarding "sectors" of a circle,
go to "Area of Sectors in Circles" before continuing with this page.

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definition
Sector of a circle: A sector of a circle is the portion of a circle enclosed by two radii and an arc. It resembles a "pizza" slice.


definition
Segment of a Circle: The segment of a circle is the region bounded by a chord and the arc subtended by the chord.           

While a sector looks like a "pie" slice, a segment looks like the "pie" slice with the triangular portion cut off (it's somewhat like the "crust section of the pizza slice"). The segment is the small partially curved figure left when the triangular portion of the sector is removed.
 segment

segmentbanner

You can probably "guess" what the formula for finding the area of a segment involves.
A segment is a sector with the triangular portion removed.
Formula: Area of Segment = Area of Sector - Area of Triangle

ex

Find the area of a segment of a circle with a central angle of 120 degrees and a radius of 8 cm. Express answer to the nearest integer.

segmentA
Solution:
Start by finding the area of the sector.
segmentAf

Now, find the area of the triangle. Dropping the altitude from the center forms a 30-60-90 degree triangle. Using the 30-60-90 rules (or trigonometry), find the altitude, which is 4, and the other leg, which is 4rad3 or 6.92820323.

segmentA3

segment8
segmentA2
AAT


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