1. Year 9 Mathematics Polygons
Polygons

2. Learning Intentions Identify polygons and non-polygons
Name polygons based on the number of sides or angles
Understand what is meant by a regular polygon
Know the formula for the sum of the interior angles of a polygon
Calculate the interior angles of polygons
Calculate exterior angles of polygons

3. Identifying Polygons
The word polygon comes from the Greek words πολύς (meaning many) and γωνία (meaning angle). A polygon is a shape with many angles.
For a shape to be considered a polygon it must be a closed shape and have straight sides.
The examples below show some shapes. Which of these shapes are polygons?

4. Naming Polygons
Polygons are given names depending on the number of angles they have.
Sometimes these names are in Latin an sometimes these names are in Greek. It is important not to confuse the two!
The table lists the names for the shapes.
Copy the table and draw each of the shapes.

5. Polygon Names Name No. of Angles Shape Triangle Heptagon Quadrilateral
Octagon
Pentagon
Nonagon
Hexagon
Decagon

6. Interior Angles
We can calculate the sum of the interior angles of a polygon by dividing the shape into triangles and counting the number of triangles.
The hexagon shown below has been divided into 4 triangles so the sum of the interior angles is 4 x 180O = 720O.
Go back to your previous table and complete the final column showing the sum of the interior angles.

7. Interior Angles of Regular Polygons
A regular polygon has all the sides the same length and all the angles the same size.
We can therefore create a formula to calculate the size of each interior angle.
Remember that we can divide a shape into 2 triangles less than the number of angles in a shape. A hexagon (6 sides) has 4 triangles.
So, if n is the number of angles (or sides) the
sum of the Interior angles = (n – 2) x 180
Or for a regular polygon
Each Interior angle =

8. Exterior Angles of Regular Polygons
The exterior angles of a polygon always add to 360O.
So, if n is the number of angles (or sides) the
sum of the Exterior angles = 360
And for a regular polygon
Each Exterior angle =

9. Calculating the Number of Sides
We can calculate the number of sides of a regular polygon using this formula also
Remember: for a regular polygon, the size of each Exterior angles =
If we rearrange this formula we get
For example, if each exterior angle is 90
We have a quadrilateral!