# Apothem

Written by Jerry Ratzlaff on . Posted in Geometry

• Apothem is the length of a line perpendicular from the center to the midpoint of the side of a regular polygon.
• A irregular polygon has no center so there can be no apothem.

$$A= r cos {\left( \frac {180} {n} \right)}$$

Where:

$$A$$ = apothem

$$r$$ = radius

$$cos$$ = cosine in degrees

$$n$$ = number of sides

## Given Edge formula

$$A=\frac {s} {2 tan \left( \frac {180} {n} \right) }$$

Where:

$$A$$ = apothem

$$s$$ = edge (side length)

$$tan$$ = tangent in degrees

$$n$$ = number of sides