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.
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
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:
