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MatematikaRia.com

# 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)

## Types of Polygons

### Simple or Complex

A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself!

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

### Concave or Convex

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

If there are any internal angles greater than 180° then it is concave. (Think: concave has a "cave" in it)

 Convex Concave

### Regular or Irregular

If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular

 Regular Irregular

## More Examples

 Complex Polygon (a "star polygon", in this case, a pentagram) Concave Octagon Irregular Hexagon

## Names of Polygons

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

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