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."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°.