MATHEMATICS;SECTORS AND SEDMENTS,PRELUDE TO CORCLE GEOMETRY

SEGMENTS AND SECTORS 

Slices

There are two main "slices" of a circle:

The "pizza" slice is called a Sector.
And the Segment, which is cut from the circle by a "chord" (a line between two points on the circle).

Try Them!

Sector	Segment

Common Sectors

The Quadrant and Semicircle are two special types of Sector:

Half a circle is
a Semicircle.

Quarter of a circle is
a Quadrant.

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: we are using radians for the angles.

This is the reasoning:

A circle has an angle of 2π and an Area of:πr²

A Sector has an angle of θ instead of 2π so its Area is :θ2π × πr²

Which can be simplified to:θ2 × r²

 

Area of Sector = θ2 × r²   (when θ is in radians)

Area of Sector = θ × π360 × r²   (when 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 reason, but the result is a slight modification of the Sector formula:

Area of Segment = θ − sin(θ)2 × r²   (when θ is in radians)

Area of Segment = ( θ × π360 − sin(θ)2 ) × r²   (when θ is in degrees)

 

Arc Length

The arc length (of a Sector or Segment) is:

L = θ × r   (when θ is in radians)

L = θ × π180 × r   (when θ is in degrees)

 

 

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