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MatematikaRia.com


Circle Sector and Segment
Slices
There are two main "slices" of a circle:
The "pizza" slice is called a Sector.
And the slice made by a chord is called a Segment. 

Common Sectors
The Quadrant and Semicircle are two special types of Sector:

Quarter of a circle is called a Quadrant.
Half a circle is called a Semicircle. 

Area of a Sector
You can work out the Area of a Sector by comparing its angle to the angle of a full circle.
Note: I am using radians for the angles. 

This is the reasoning:
 A circle has an angle of 2π and an Area of: πr^{2}
 So a Sector^{} with an angle of θ (instead of 2π) must have an area of: (θ/2π) × πr^{2}
 Which can be simplified to: (θ/2) × r^{2}
Area of Sector = ½ × θ × r^{2}
= ½ × (θ × π/180) × r^{2} (if θ is in degrees) 

Arc Length of Sector or Segment
By the same reasoning, the arc length (of a Sector or Segment) is:
Arc Length "L" = θ × r
= (θ × π/180) × r (if θ is in degrees) 
Area of Segment
The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here).
There is a lengthy derivation, but the result is a slight modification of the Sector formula: 

Area of Segment = ½ × (θ  sin θ) × r^{2}
= ½ × ( (θ × π/180)  sin θ) × r^{2} (if θ is in degrees) 


