# Polygons

## 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

tr>
Name Sides Shape Interior Angle If it is a Regular Polygon... 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

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