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)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)
 

 

  

 

 

 

 

 

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