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

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.

a = 6/2 = 3 cm

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 of a Regular Hexagon

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

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.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.