Regular Polygon formula

Math

Trigon n = 3 x = 60° y= 120°	Tetragon n = 4 x = 90° y= 90°	Pentagon n = 5 x = 108° y= 72°
Hexagon n = 6 x = 120° y= 60°	Heptagon n = 7 x = 128,57° y= 51,43°	Octagon n = 8 x = 135° y= 45°
Nonagon n = 9 x = 140° y= 40°	Decagon n = 10 x = 144° y= 36°	Undecagon n = 11 x = 144,27° y= 32,73°
Dodecagon n = 12 x = 150° y= 30°	Tridecagon n = 13 x = 152,31° y= 27,69°	Tetradecagon n = 14 x = 154,29° y= 25,71°
n = number of sides
Side Length a a = 2r tan(π/n) a = 2R sin(π/n)	Perimeter P P = na	Area A A = (1/4)na² cot(π/n) A = nr tan(π/n)
Angles x + y = 180°	Interior Angle x x = (n-2)π / n radians x = (n-2)/n) x 180° degrees x = 180 - y	Exterior Angle y y = (2π / n) radians y = (360° / n) degrees y = 180 - x
Inradius r (apothem) r = (1/2)a cot(π/n) r = R cos(π/n)	Circumradius R R = (1/2) a csc(π/n) R = r sec(π/n)