Polygons - Math Is Fun

Polygons

A polygon is a plane shape with straight sides.

Is it a Polygon?

A polygon is a flat 2-dimensional (2D) shape made of straight lines. The sides connect to form a closed shape. There are no gaps or curves.

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".

Example: Stop Sign

A stop sign is an example of a regular polygon.

It has eight equal sides and angles, making it a regular octagon.

Can you think of more polygons in real life?

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 inward-pointing angles: internal angles are at most 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 a single, unbroken boundary, and it doesn't cross over itself. A complex polygon has sides that intersect, making many polygon rules invalid.

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°
Hectogon	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 Hecto... 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

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 "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

629, 630, 633, 634, 2125, 2126, 3255, 3256, 2127, 3257 Interactive Polygons Interior Angles of Polygons Exterior Angles of Polygons 2D Shapes (simpler page) Copyright © 2025 Rod Pierce