The Lesson
A polygon is a 2-dimensional shape with straight sides.
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."
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°.
)