The Lesson

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

Dictionary Definition

The Oxford English Dictionary defines a polygon as "a plane figure with many (usually more than four) straight sides and the same number of angles."

Lesson Slides

The slider below shows more about polygons.

Regular Polygons

Regular polygons have sides of equal length and equal angles.
Shape Name Number of sides
Triangle (or Trigon) A regular triangle is an equilateral triangle 3
Quadrilateral (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 sides of different lengths and different angles.
Shape Name Number of sides
Irregular Quadrilateral 4
Irregular Hexagon 6
Irregular Octagon 8

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:

In this formula, n is the number of sides of the polygon. For example, a hexagon has 6 sides, so n = 6. Putting this into the formula gives:

Sum of interior angles = (n − 2) × 180°

Sum of interior angles = (6 − 2) × 180°

Sum of interior angles = 4 × 180°

Sum of interior angles = 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°.