Regular Polygons and Symmetry

Regular Polygon

A regular Polygon is both equilateral (all sides congruent) and equiangular (all angles congruent).

Line Symmetry

A regular Polygon with n sides has n lines of symmetry.

• Equilateral Triangle: 3 lines of symmetry
• Square: 4 lines of symmetry
• Regular hexagon: 6 lines of symmetry

Rotational Symmetry

A regular n-gon has rotational symmetry of order n. The smallest rotation Angle that maps it onto itself is 360°/n.

Center and Apothem

• The center of a regular Polygon is equidistant from all vertices (circumradius) and from all sides (apothem).
• The apothem is the perpendicular distance from the center to a side.
• Area = (1/2) × apothem × perimeter