Regular Polygons

A regular polygon has equal angles and sides.

Regular Polygon

Regular polygons can be inscribed in circles.

Elements of a Regular Polygon

Regular Polygon

Center

The center is the inner point equidistant from each vertex.

Radius

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

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

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

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

Exterior Angle of a Regular Polygon

formula of area of a regular polygon

Example

Calculate the perimeter and area of the hexagon:

Area of a regular polygon

fórmulas

fórmulas