Circular sector area

The sector of a circle is a region bounded by two straight line segments that run from the center to the circumference. These line segments are the radii of the circle, see the figure:

Angle α is called the central angle.
Thus, we realize that the circular sector is a part of the circular region, that is, it is a fraction of the circle's area. Thus, we can say that the area of ​​the circular sector is directly proportional to the value of α, since the area of ​​the entire circle is directly proportional to 360º.
So we can set up the following relationship (rule of three):
Sector area α
360° circle area
Sector = α
πr² 360°
Sector 360° = α. πr²
Asector = α. πr²
360°
Example: Determine the area of ​​the circular sector of radius 6cm whose central angle measures:
• 60°
Sector = 60°. π6²
360°
Sector = 60°. π 36 
360°
Sector = 6π cm²
• π/2
π/2 corresponds to 90°
Sector = 90°. π6²
360°
Sector = 90°. π36
360°
Sector = 9π cm²

by Danielle de Miranda
Graduated in Mathematics
Brazil School Team

Spatial Metric Geometry -Math - Brazil School

Source: Brazil School - https://brasilescola.uol.com.br/matematica/area-setor-circular.htm

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