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
If all angles are equal and all sides are equal, then it is regular, 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) |
| 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.
Now, let's have some fun! Try to sing this song so you can memorize our lesson easily!
Before you leave this page, can you name a thing you usually use that resembles a polygon? Please leave your answer in a comment box.Thank you!
