Polygons
A polygon is a plane shape with straight sides.
Is it a Polygon?
Polygons are 2dimensional 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  10^{100}  ~180°  
ngon  n  (n−2) × 180° / n 
You can make names using this method:

 
Example: a 62sided polygon is a Hexacontadigon 
BUT, for polygons with 13 or more sides, it is OK (and easier) to write "13gon", "14gon" ... "100gon", 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 "Sevenagon"
Octagon (8 Sides)
An Octopus has 8 tentacles
Nonagon (9 Sides)
Think Nonagon is a "Nineagon"
Decagon (10 Sides)
Think Decagon has 10 sides,
just like our Decimal system has 10 digits