Polygons

A polygon is a plane shape with straight sides.

Is it a Polygon?

Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).

Polygon
(straight sides)
Not a Polygon
(has a curve)
Not a Polygon
(open, not closed)

Polygon comes from Greek. Poly- means "many" and -gon means "angle".

Types of Polygons

Regular or Irregular

A regular polygon has all angles equal and all sides equal, otherwise it is irregular

 
Regular   Irregular

 

Concave or Convex

A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.

If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it)

 
Convex   Concave

 

Simple or Complex

A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself! Many rules about polygons don't work when it is complex.

 
Simple Polygon
(this one's a Pentagon)
  Complex Polygon
(also a Pentagon)

 

More Examples

   
Irregular Hexagon

  Concave Octagon

  Complex Polygon
(a "star polygon",
in this case a pentagram)

 

Play With Them!

Try Interactive Polygons ... make them regular, concave or complex.

Names of Polygons

    If it is a Regular Polygon...
Name Sides Shape Interior Angle
Triangle (or Trigon) 3 60°
Quadrilateral (or Tetragon) 4 90°
Pentagon 5 108°
Hexagon 6 120°
Heptagon (or Septagon) 7 128.571°
Octagon 8 135°
Nonagon (or Enneagon) 9 140°
Decagon 10 144°
Hendecagon (or Undecagon) 11 147.273°
Dodecagon 12 150°
Triskaidecagon 13   152.308°
Tetrakaidecagon 14   154.286°
Pentadecagon 15   156°
Hexakaidecagon 16   157.5°
Heptadecagon 17   158.824°
Octakaidecagon 18   160°
Enneadecagon 19   161.053°
Icosagon 20   162°
Triacontagon 30   168°
Tetracontagon 40   171°
Pentacontagon 50   172.8°
Hexacontagon 60   174°
Heptacontagon 70   174.857°
Octacontagon 80   175.5°
Enneacontagon 90   176°
Hectagon 100   176.4°
Chiliagon 1,000   179.64°
Myriagon 10,000   179.964°
Megagon 1,000,000   ~180°
Googolgon 10100   ~180°
n-gon n (n-2) × 180° / n

You can make names using this method:

Sides
  Start with...
20
  Icosi...
30
  Triaconta...
40
  Tetraconta...
50
  Pentaconta...
60
  Hexaconta...
70
  Heptaconta...
80
  Octaconta...
90
  Enneaconta...
100   Hecta...
etc..    
Sides
  ...end with
+1
  ...henagon
+2
  ...digon
+3
  ...trigon
+4
  ...tetragon
+5
  ...pentagon
+6
  ...hexagon
+7
  ...heptagon
+8
  ...octagon
+9
  ...enneagon

Example: a 62-sided polygon is a Hexacontadigon

BUT, for polygons with 13 or more sides, it is OK (and easier) to write "13-gon", "14-gon" ... "100-gon", etc.

Remembering

Quadrilateral (4)


A Quad Bike has 4 wheels

Pentagon (5)


The "Pentagon" in Washington DC has 5 sides

Hexagon (6)

Think Hexagon is a "Six-agon"

Octagon (8)


An Octopus has 8 tentacles

Nonagon (9)

Think Nonagon is a "Nine-agon"

Decagon (10)

Think Decagon has 10 sides,
just like our Decimal system has 10 digits