This post looks at various elements of a circle including: radius, diameter, circumference, arc, chord, tangent, segment, sector and also how to work out the area of a segment and a sector.

Arc lengths & Sector/Segments areas

Arc Length
The area of a circle is found in this article.
Area of Sector

As for the Area of a Segment in a circle, this is derived by subtracting one shape from another shape. If you consider the sector that includes the segment and then take away the triangle formed by the two radii and the chord of the segment, you will end up with the segment. This short video explain this process with an example.

Shapes - Polygons
Shapes - Areas