
Sides of a Regular Polygon
The sides of a regular polygon are the line segments that make it up.
Try this
Adjust the regular polygon below by dragging any orange dot, or alter the number of sides. The length of the sides
will change.
The formulas below give the length of the side of regular polygon given the number of sides
and either the radius or apothem.
Side length given the apothem (inradius)
If you know the apothem (distance from the center of the polygon to the midpoint of any side  see figure above)

where:
a is the length of the apothem (inradius)
n is the number of sides
tan is the tangent function calculated in degrees
(see Trigonometry Overview)


Side length given the radius (circumradius):
If you know the radius
(distance from the center to a vertex):

where:
r is the radius (circumradius)
n is the number of sides
sin is the sine function calculated in degrees
(see Trigonometry Overview)


Irregular polygons
The sides of an irregular polygon are essentially random lengths. There is no formula to calculate their lengths.
In the figure above, uncheck 'regular' to see this.
Related polygon topics
General
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
Named polygons
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