Defining & Naming Polygons
A polygon is a closed, flat figure made of straight segments. From triangles to dodecagons, naming depends on the number of sides.
Introduction
Polygons are everywhere — stop signs, floor tiles, soccer balls. Understanding their names, types, and properties is the foundation for studying quadrilaterals, area, and beyond.
Past Knowledge
Lines & segments (1.1). Triangles (Unit 5). Angles.
Today's Goal
Name polygons by side count, classify as convex/concave and regular/irregular.
Future Success
Angle sums (9.1.2–9.1.3), quadrilaterals (9.2–9.3), area formulas (Unit 10).
Key Concepts
What Makes a Polygon?
- Closed — starts and ends at the same point
- Flat — lies entirely in one plane
- Straight sides — no curves
- No crossing sides — sides don't intersect except at vertices
Naming Chart
| Sides | Name | Sides | Name |
|---|---|---|---|
| 3 | Triangle | 8 | Octagon |
| 4 | Quadrilateral | 9 | Nonagon |
| 5 | Pentagon | 10 | Decagon |
| 6 | Hexagon | 11 | Hendecagon |
| 7 | Heptagon | 12 | Dodecagon |
For , just say “-gon” (e.g., 15-gon).
Classification
- Convex: All interior angles < 180°. No side “caves in.”
- Concave: At least one interior angle > 180° (a “reflex” angle). Has a “dent.”
- Regular: All sides equal AND all angles equal (equilateral + equiangular)
- Irregular: Not all sides or not all angles are equal
Polygon Gallery
Worked Examples
Name That Polygon
A figure has 6 equal sides and 6 equal angles. Name and classify it.
6 sides → hexagon
All sides equal + all angles equal → regular
Regular hexagon
Convex or Concave?
A pentagon has interior angles 100°, 110°, 95°, 130°, 285°. Is it convex or concave?
285° > 180° → there is a reflex angle
Concave — the 285° angle creates a “dent”
Diagonals Count
How many diagonals does a decagon (10-gon) have?
Formula:
35 diagonals
Common Pitfalls
Thinking Regular Means Convex
All regular polygons ARE convex, but not all convex polygons are regular. A rectangle is convex but not regular (sides aren't all equal).
Open Figures Are NOT Polygons
If the figure doesn't close, it's not a polygon. A “V” shape made of two segments is NOT a polygon.
Real-Life Applications
Architecture — The Pentagon
The U.S. Department of Defense headquarters is literally a regular pentagon, one of the world's largest office buildings.
Nature — Honeycomb
Bees build hexagonal cells because regular hexagons tessellate perfectly, using the least wax for the most storage space.
Practice Quiz
Loading...