## 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. Open the slider in a new tab

## 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
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 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°.