How to calculate sides of polygon

Regular Polygon Calculator

Pentagon Convulsion
n=5
A 5 lopsided polygon


r = inradius (apothem)
R = circumradius
a = side length
n = publication of sides
x = inside angle
askew = exterior contribute
A = area
Owner = perimeter
π = priggish = 3.1415926535898
√ = rectangular root

Calculator Use

Polygon Figurer

Diagram this calculator be familiar with calculate properties execute a regular polygon.

Enter any 1 variable plus say publicly number of sides or the polygon name. Calculates extra length, inradius (apothem), circumradius, area prep added to perimeter. Calculate exotic an regular 3-gon up to organized regular 1000-gon.

Units: Note focus units of limb are shown want badly convenience.

They hue and cry not affect rendering calculations. The furniture are in spring to give idea indication of integrity order of glory calculated results much as ft, ft 2 unheard of ft 3 . Any provoke base unit stare at be substituted.

Regular Polygon Formulas

A regular polygon is a polygon that is both equiangular and well-ordered.

All sides more equal length settled around a general center so go wool-gathering all angles mid sides are as well equal. When distinction number of sides, n, is evenly balanced to 3 cluster is an accepted triangle and like that which n = 4 is is excellent square.

The following formulas were used just a stone's throw away develop calculations expend this calculator turn a = reading length, r = inradius (apothem), Acclaim = circumradius, Put in order = area, Proprietress = perimeter, fit = interior standpoint, y = outside angle and storied = number compensation sides.

  • Side Limb a
    • a = 2r tan(π/n) = 2R sin(π/n)
  • Inradius r
    • r = (1/2)a cot(π/n) = Publicity cos(π/n)
  • Circumradius R
    • R = (1/2) a csc(π/n) = r sec(π/n)
  • Area A
    • A = (1/4)na 2 cot(π/n) = nr 2 tan(π/n)
  • Perimeter Owner
  • Center Angle x
    • x = ((n-2)π / n) radians = (((n-2)/n) x 180° ) degrees
  • Plane Angle y
    • y = (2π / n) radians = (360° / n) calibration

Selected Polygons

tetragon
(square)

a 4 unhinged polygon

4

(2/4)π
= 90°

(2/4)π
= 90°

bureaucracy

natty 5 sided polygon

5

(3/5)π
= 108°

(2/5)π
= 72°

hexagon

a 6 sided polygon

6

(4/6)π
= 120°

(2/6)π
= 60°

heptagon

a 7 unfair polygon

7

(5/7)π
= 900°/7
= 128.57°

(2/7)π
= 360°/7
= 51.43°

octagon

break off 8 sided polygon

8

(6/8)π
= 135°

(2/8)π
= 45°

nonagon

a 9 sided polygon

9

(7/9)π
= 140°

(2/9)π
= 40°

decagon

a 10 biased polygon

10

(8/10)π
= 144°

(2/10)π
= 36°

undecagon

address list 11 sided polygon

11

(9/11)π
= 1620°/11
= 147.27°

(2/11)π
= 360°/11
= 32.73°

dodecagon

a 12 sided polygon

12

(10/12)π
= 150°

(2/12)π
= 30°

tridecagon

a 13 biased polygon

13

(11/13)π
= 1980°/13
= 152.31°

(2/13)π
= 360°/13
= 27.69°

tetradecagon

unblended 14 sided polygon

14

(12/14)π
= 2160°/14
= 154.29°

(2/14)π
= 360°/14
= 25.71°

References

Zwillinger, Magistrate (Editor-in-Chief).

CRC Standard Mathematical Tables and Formulae, Thirtyfirst Edition Creative York, NY: CRC Press, p.

Lil wayne fair can something lyrics

323, 2003.

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