# Regular Polygons

A regular polygon has equal angles and sides.

Regular polygons can be inscribed in circles.

### Elements of a Regular Polygon

#### Center

The center is the inner point equidistant from each vertex.

The radius, r, is the segment that goes from the center to each vertex.

#### Apothem

The apothem, a, is the distance from the center to the midpoint of one side.

## Angles of a regular polygon

#### Central Angle of a Regular Polygon

The central angle of a regular polygon is formed by two consecutive radius.

If n is the number of sides of a polygon:

Central angle = 360° : n

Central angle of a regular pentagon = 360°: 5 = 72º

#### Interior Angle of a Regular Polygon

The interior angle of a regular polygon is formed by two consecutive sides.

Interior angle = 180° − central angle

Interior angle of a regular pentagon = 180° − 72° = 108º

#### Exterior Angle of a Regular Polygon

The exterior angle of a regular polygon is formed by a side and the extension of a consecutive side.

The exterior and interior angles are supplementary, that is to say, that add up 180º.

Exterior angle = central angle

Exterior angle of a regular pentagon = 72º

# Perimeter of a regular polygon

The perimeter is equal to the sum of the lengths of all sides or the length of a side multiplied by the number of sides.

P = n · l

# Area of a regular polygon

#### Example

Calculate the perimeter and area of the hexagon: