What is the number of sides of regular polygon if each of its interior angle is 3π 4 Radian?

Get a Widget for this Calculator

r = inradius (apothem) R = circumradius a = side length n = number of sides x = interior angle y = exterior angle A = area P = perimeter

π = pi = 3.1415926535898

Calculator Use

Polygon Calculator

Use this calculator to calculate properties of a regular polygon. Enter any 1 variable plus the number of sides or the polygon name. Calculates side length, inradius (apothem), circumradius, area and perimeter. Calculate from an regular 3-gon up to a regular 1000-gon.

Units: Note that units of length are shown for convenience. They do not affect the calculations. The units are in place to give an indication of the order of the calculated results such as ft, ft2 or ft3. Any other base unit can be substituted.

Regular Polygon Formulas

A regular polygon is a polygon that is both equiangular and equilateral. All sides are equal length placed around a common center so that all angles between sides are also equal. When the number of sides, n, is equal to 3 it is an equilateral triangle and when n = 4 is is a square.

The following formulas were used to develop calculations for this calculator where a = side length, r = inradius (apothem), R = circumradius, A = area, P = perimeter, x = interior angle, y = exterior angle and n = number of sides.

• Side Length a
  • a = 2r tan(π/n) = 2R sin(π/n)
• Inradius r
  • r = (1/2)a cot(π/n) = R cos(π/n)
• Circumradius R
  • R = (1/2) a csc(π/n) = r sec(π/n)
• Area A
  • A = (1/4)na2 cot(π/n) = nr2 tan(π/n)
• Perimeter P
• Interior Angle x
  • x = ((n-2)π / n) radians = (((n-2)/n) x 180° ) degrees
• Exterior Angle y
  • y = (2π / n) radians = (360° / n) degrees
  • 

Selected Polygons

tetragon
(square)

a 4 sided polygon

pentagon

a 5 sided polygon

hexagon

a 6 sided polygon

heptagon

a 7 sided polygon

(5/7)π = 900°/7

= 128.57°

octagon

an 8 sided polygon

nonagon

a 9 sided polygon

decagon

a 10 sided polygon

undecagon

an 11 sided polygon

(9/11)π = 1620°/11

= 147.27°

(2/11)π = 360°/11

= 32.73°

dodecagon

a 12 sided polygon

tridecagon

a 13 sided polygon

(11/13)π = 1980°/13

= 152.31°

(2/13)π = 360°/13

= 27.69°

tetradecagon

a 14 sided polygon

(12/14)π = 2160°/14

= 154.29°

(2/14)π = 360°/14

= 25.71°

References

Zwillinger, Daniel (Editor-in-Chief). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, p. 323, 2003.

Weisstein, Eric W. "Regular Polygon." From MathWorld--A Wolfram Web Resource. Regular Polygon.