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Area of a Pentagon

There are 2 formulas for finding the area of a pentagon. The first only needs the side length; the second also uses the apothem.

Using the Side Length

When you only know the length of one side, use this formula:

Pentagon area formula using side length
Aarea of the pentagon 5number of sides tlength of each side tantangent function (in radians)

Using the Apothem

If you also know the apothem, you can use either of these equivalent expressions:

Pentagon area formula using apothem
Pentagon area formula variants
Aarea of the pentagon Pperimeter of the pentagon aapothem length 5number of sides tlength of each side

Both expressions are equivalent and give the same result.

What Is the Apothem?

In a regular polygon like the pentagon, the apothem is the shortest distance from the center to any of its sides. The image below shows this clearly:

Apothem of a Pentagon

More About the Pentagon

Click on any element to learn more.

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