GEOMETRY

Properties Of Polygons

Learn the reliable method for properties of polygons, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Polygon questions depend on exact properties such as sides, angles and parallel lines.

Picture itCount sides and vertices
Colourful playground markings showing shapes, equal sections, parallel lines and boundaries
2 · THE METHOD

Follow these steps

  1. Name the polygon from its defining features.
  2. Use only properties guaranteed for that polygon.
  3. Apply an angle rule if a missing angle or total is required.
3 · WORKED EXAMPLES

See the method in action

Example 1

The 8-sided polygon shown is regular. What is the size of one exterior angle?

8 sides?
  1. The exterior angles make one full turn.
  2. Since the 8 exterior angles are equal, each is 360° ÷ 8 = 45°.
Answer: 45°
Example 2

The 10-sided polygon shown is regular. What is the size of one exterior angle?

10 sides?
  1. The exterior angles make one full turn.
  2. Since the 10 exterior angles are equal, each is 360° ÷ 10 = 36°.
Answer: 36°
4 · ELEVENSPRINT TIP

A useful shortcut

Apply an angle rule if a missing angle or total is required.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.