What Is a Polygon?

A polygon is a 2-dimensional shape with straight sides.

Regular Polygons

Regular polygons have equal sides and equal angles.

Shape Name Number of sides
Triangle
(or Trigon)

A regular triangle is an equilateral triangle
3
(or Tetragon)

A regular quadrilateral is a square
4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Dodecagon 12

Irregular Polygons

Irregular polygons have different length sides and different angles.

Shape Name Number of sides
Irregular Hexagon 6
Irregular Octagon 8

Geometry Lessons
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Note
WHAT'S IN A NAME?

Polygon comes from the Greek 'poly-', meaning "many", and '-gon', meaning "angle".

Therefore 'polygon' means "many angles" as each polygon has several angles inside of it.

INTERIOR ANGLES

The angles between the sides in a polygon, inside the shape, are called interior angles.

There is a formula for the sum of the interior angles of a polygon:

where n is the number of sides of the polygon.

For example, a hexagon has 6 sides, so n = 6. Putting this into the forula gives:

(n - 2) × 180° =

(6 - 2) × 180° =

4 × 180° =

720°

The angles in a hexagon add up to 720°

EXTERIOR ANGLES

The angles between the sides in a polygon, outside the shape, are called exterior angles.

The exterior angles always add up to 360°.