About Apothem Calculator (Formula)
An Apothem Calculator is a tool used to calculate the apothem of a regular polygon. The apothem is a line segment drawn from the center of the polygon to the midpoint of a side, perpendicular to that side. It’s a fundamental geometric parameter used to calculate the area and other properties of regular polygons.
The formula for calculating the apothem of a regular polygon depends on the type of polygon:
For a Regular Polygon with n sides: Apothem (a) = (Side Length) / (2 * tan(π / n))
Where:
- Apothem (a) is the distance from the center of the polygon to the midpoint of a side.
- Side Length is the length of one of the sides of the regular polygon.
- π (pi) is a constant approximately equal to 3.14159.
- n is the number of sides of the regular polygon.
To use the Apothem Calculator formula, follow these steps:
- Determine the length of one of the sides of the regular polygon (Side Length).
- Determine the number of sides of the regular polygon (n).
- Plug the values of side length (Side Length) and number of sides (n) into the formula: Apothem (a) = (Side Length) / (2 * tan(π / n)).
- Calculate the apothem of the regular polygon.
The apothem is particularly useful when calculating the area of regular polygons, as the area can be expressed as the product of the apothem and the perimeter. Additionally, the apothem helps define the relationship between the radius of the circumcircle (circle that passes through all vertices) and the side length of the polygon.
Regular polygons include shapes like triangles, squares, pentagons, hexagons, and so on, where all sides and angles are congruent.