# Apothem of a Regular Polygon

## Apothem of a Regular Polygon

Distance from the centre of the polygon to any side of the polygon.

The word “apothem” also refers to the line segment drawn perpendicularly from the centre of the polygon to one of its sides.

### Formula

• The general formula to find the length $$a$$ of the apothem of a regular polygon with $$n$$ sides that have a length of $$c$$ is: $$a=\dfrac{c}{2\textrm{tan}({\frac{180}{n})}}$$.

• The length $$a$$ of the apothem of a regular polygon with n sides can also be expressed using the measure of the radius of the circle circumscribed around the polygon:

$$a=r \cos{( \frac{180}{n})}$$.