Regular Polygon formula
Trigon n = 3 x = 60° y= 120° |
Tetragon n = 4 x = 90° y= 90° |
Pentagon n = 5 x = 108° y= 72° |
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Hexagon n = 6 x = 120° y= 60° |
Heptagon n = 7 x = 128,57° y= 51,43° |
Octagon n = 8 x = 135° y= 45° |
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Nonagon n = 9 x = 140° y= 40° |
Decagon n = 10 x = 144° y= 36° |
Undecagon n = 11 x = 144,27° y= 32,73° |
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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° |
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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)naČ 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) |