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:
|
 |
|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
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 Sides)
A Quad Bike has 4 wheels
Pentagon (5 Sides)
The "Pentagon" in Washington DC has 5 sides
Hexagon (6 Sides)
Honeycomb has Hexagons
Septagon (7 Sides)
Think Septagon is a "Seven-agon"
Octagon (8 Sides)
An Octopus has 8 tentacles
Nonagon (9 Sides)
Think Nonagon is a "Nine-agon"
Decagon (10 Sides)
Think Decagon has 10 sides,
just like our Decimal system has 10 digits