Chapters

A regular pentagon is a polygon with five equal sides and angles.

## Angles of the Pentagon

The sum of interior angles of a pentagon = (5 − 2) · 180° = **540°**

The value of an interior angle of a regular pentagon is: 540º : 5 = **108º**

The central angle of a regular pentagon measures: 360º : 5 = **72º**

## Diagonals of the Pentagon

The number of diagonals in a regular pentagon = 5 · (5 − 3) : 2 = **5**

## Apothem of the Regular Pentagon

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

## Perimeter of a Regular Pentagon

**Perimeter = 5 · l**

## Area of a Regular Pentagon

## Example

Calculate the apothem, perimeter and area of a regular pentagon with a side of 6 cm.

**P = 5 · 6 = 30 cm**

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