What is a Polygon?
A closed plane figure made up of several line segments that are joined together. The sides do not cross each other. Exactly two
sides meet at every vertex.
Types | Formulas | Parts | Special Polygons | Names
Types of Polygons
Regular - all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral.
Equiangular - all angles are equal.
Equilateral - all sides are the same length.
Convex - a straight line drawn through a convex polygon crosses at most two sides. Every interior angle is
less than 180°. OR A polygon is convex if no line that contains a side of the polygon contains a point on the
interior of the polygon.
Concave (or nonconvex) - you can draw at least one straight line through a concave polygon that crosses
more than two sides. At least one interior angle is more than 180°.
Polygon Formulas
(N = # of sides)
Sum of the interior angles of a polygon = (N - 2) x 180°
The number of diagonals in a polygon = 1/2 N(N-3)
The number of triangles (when you draw all the diagonals from one vertex) in a polygon = (N - 2)
Polygon Parts
Side - one of the line segments that make up the polygon.
Vertex - point where two sides meet. Two or more of these points are
called vertices.
Diagonal - a line connecting two vertices that isn't a side.
Interior Angle - Angle formed by two adjacent sides inside the polygon.
Exterior Angle – the angle formed when extending one side. It is the
supplement of the interior angle (not labeled well on this picture)
Special Polygons
Special Quadrilaterals - square, rhombus, parallelogram, rectangle, and the trapezoid.
Special Triangles - right, equilateral, isosceles, scalene, acute, obtuse.
Polygon Names
Generally accepted names
Sides
Name
n
N-gon
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
12
Dodecagon
Names for other polygons have been proposed.
Sides
9
Name
Nonagon, Enneagon
11
Undecagon, Hendecagon
13
Tridecagon, Triskaidecagon
14
Tetradecagon, Tetrakaidecagon
15
Pentadecagon, Pentakaidecagon
16
Hexadecagon, Hexakaidecagon
17
Heptadecagon, Heptakaidecagon
18
Octadecagon, Octakaidecagon
19
Enneadecagon, Enneakaidecagon
20
Icosagon
30
Triacontagon
40
Tetracontagon
50
Pentacontagon
60
Hexacontagon
70
Heptacontagon
80
Octacontagon
90
Enneacontagon
100
Hectogon, Hecatontagon
1,000
Chiliagon
10,000
Myriagon
To construct a name, combine the prefix+suffix
Sides
Prefix
Sides
Suffix
20
Icosikai...
+1
...henagon
30
Triacontakai...
+2
...digon
40
Tetracontakai...
+3
...trigon
50
Pentacontakai...
+4
...tetragon
60
Hexacontakai...
+5
...pentagon
70
Heptacontakai...
+6
...hexagon
80
Octacontakai...
+7
...heptagon
90
Enneacontakai...
+8
...octagon
+9
...enneagon
+
Examples:
46 sided polygon - Tetracontakaihexagon
28 sided polygon – Icosikaioctagon
However, many people use the form n-gon, as in 46-gon, or 28-gon instead of these
names.
Here is a chart for the interior angles…
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Octagon
Decagon
n-gon
Number of
Sides
Number of
Triangles
Sum of the
measures of
angles
Measure of
one interior
angle