Polygons
Introduction:
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
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
| | 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 | 7 | | 128.571° |
Octagon | 8 | | 135° |
Nonagon (or Enneagon) | 9 | | 140° |
Decagon | 10 | | 144° |
Hendecagon (or Decagon) | 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 |...