Segment
A portion of a Circle whose upper boundary is a circular Arc and whose lower boundary is a Chord making aCentral Angle 
radians (180°), illustrated above as the shaded region. Let 
be the radius of theCircle, 
the Chord length, 
the Arc Length, 
the height of the arced portion, and 
the heightof the triangular portion. Then
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
|  | (4) | |
|  | (5) | |
 | |  | (6) |
|  | (7) | |
|  | (8) | |
|  | (9) |
The Angle
obeys the relationships | |  | |
|  | (10) |
The Area of the segment is then
 | |  | (11) |
|  | (12) | |
|  | (13) | |
|  | (14) | |
|  | (15) |
where the formula for the Isosceles Triangle in terms of the Vertex angle has been used (Beyer 1987).See also Chord, Circle-Circle Intersection, Cylindrical Segment, Lens,Parabolic Segment, Sagitta, Sector, Spherical Segment
References
Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 125, 1987.
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