section_path: Properties and formulas/Area/Regular polygons
section_name: Regular polygons
paragraph_text: Regular polygons
  
  Many specialized formulas apply to the areas of regular polygons.
  
  The area of a regular polygon is given in terms of the radius r of its inscribed circle and its perimeter p by
  
  This radius is also termed its apothem and is often represented as a.
  
  The area of a regular n -gon in terms of the radius R of its circumscribed circle can be expressed trigonometrically as:
  
  The area of a regular n -gon inscribed in a unit-radius circle, with side s and interior angle α, {\displaystyle \alpha,} can also be expressed trigonometrically as: