Apothems

The apothem of a regular polygon is the distance from the center to the midpoint of one of its sides.

Apothem of a Square

Apothem of a Square


The apothem of a square is equal to half of the length of one side.

Example

Calculate the apothem of a square with a side of 6 cm.

Apothem of a Square


a = 6/2 = 3 cm

Apothem of a Regular Polygon

Apothem of a Regular Polygon

By applying the Pythagorean theorem for one of the triangles, we obtain:

Example

Calculate the apothem of a regular pentagon with a side of 6 cm.

Apothem and Radius of a Pentagon


Apothem of a Regular Pentagon

Apothem of a Regular Pentagon

Apothem of a Regular Hexagon

Apothem and Radius of a Hexagon


The radius of a regular hexagon is equal to the side.

Apothem of a Regular Hexagon

Apply the Pythagorean theorem for the triangle:

Example

Find the apothem of a regular hexagon inscribed in a circle with a radius of 4 cm.

Apothem and Radius of a Regular Hexagon