Nonagon - Definition, Examples, Quiz, FAQ, Trivia
Learn about this special polygon with clear explanations and practice activities
What is a Nonagon?
A nonagon is a polygon with nine sides and nine angles. The name comes from two Latin words: "nona" meaning nine and "gon" meaning angle or side.
Nonagons are also called 9-gons. They can be regular (with all sides and angles equal) or irregular (with sides and angles of different sizes).
Every nonagon has nine straight sides that connect to form nine corners (vertices). The sides don't cross each other, making nonagons simple polygons.
Key Concept
A nonagon always has nine sides, nine angles, and nine vertices - that's what makes it special!
Types of Nonagons
There are two main types of nonagons:
| Type of Nonagon | Properties |
|---|---|
| Regular Nonagon |
|
| Irregular Nonagon |
|
Remember
The regular nonagon is the most common type you'll see in geometry lessons and puzzles.
Nonagon Properties
Nonagons have special mathematical properties:
Angle Formulas
Each interior angle in a regular nonagon = 1260° ÷ 9 = 140°
Each exterior angle in a regular nonagon = 360° ÷ 9 = 40°
Diagonals
A diagonal is a line connecting two non-adjacent vertices. A nonagon has:
So a nonagon has 27 diagonals!
Other Polygons
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Real-World Examples
Nonagons appear in many places once you start looking for them:
1. Architecture: Some buildings and temples have nonagon-shaped elements in their design.
2. Coins: Some countries mint nonagon-shaped coins. The Australian 50-cent coin is a famous example!
3. Star Patterns: Many star designs are based on nonagons, especially nine-pointed stars.
4. Gazebos: Some gazebos and pavilions have nine sides, creating a nonagon shape.
5. Games and Puzzles: Nonagon shapes often appear in board games and puzzle designs.
Try This
Look around your home or neighborhood for shapes with nine sides. You might be surprised where they appear!
Nonagon Quiz
Test your knowledge about nonagons with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about nonagons:
Math Trivia
Discover interesting facts about nonagons and geometry:
Ancient Geometry
The regular nonagon was studied by ancient Greek mathematicians over 2000 years ago. They discovered that constructing a perfect nonagon with only a compass and straightedge is impossible!
The Number Nine
Any number multiplied by nine has digits that sum to nine (e.g., 9×4=36 → 3+6=9). Nonagons are the only polygons with this special number of sides.
Architectural Wonder
The Tower of the Winds in Athens, built in the 1st century BCE, is one of the world's oldest nonagonal buildings. This ancient structure has survived for over 2000 years!
Coin Design
The Australian 50-cent coin is a regular nonagon, making it one of the few non-round coins in circulation. It was introduced in 1969 and is still used today.