Enter the length of any side and the total number of sides of a regular polygon (all sides and angles equal) into the calculator to determine the apothem. This calculator can also determine the side length or number of sides given the other variables (regular polygons only).
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Apothem Formula
The following formula can be used to calculate the apothem of a regular polygon (all sides and angles equal).
a = \frac{S}{2\tan(\pi/n)}- Where a is the apothem
- S is the length of any side
- n is the total number of sides
To calculate the apothem, divide the side length by 2 × tan(π/n) (angles in radians), or equivalently 2 × tan(180°/n) if using degrees.
Apothem Definition
In a regular polygon, the apothem is the perpendicular distance from the center of the polygon to the midpoint of any side (it is the radius of the inscribed circle).
Apothem Example
How to calculate the apothem of a regular polygon?
- First, determine the number of sides.
Count the total number of sides of the regular polygon. For example, a regular hexagon has six sides.
- Next, determine the length of any side.
Since the length of all sides on a regular polygon are equal, you can choose any side to measure.
- Finally, calculate the apothem.
Input the side length and number of sides into the formula to calculate the apothem.
FAQ
In a regular polygon, an apothem is the perpendicular distance from the center of the polygon to the midpoint of one of the sides (the inradius).
For a regular polygon, the apothem can be found using the formula above. It can also be found from the circumradius R using: a = R × cos(π/n).
