The number of sides a polygon has is fundamental to its definition and naming. This count is most commonly represented by the variable n, and polygons are systematically named based on this specific number of sides.
Representing the Number of Sides
When referring to the number of sides a polygon possesses, it can be written in a few ways:
- As a numerical value: For instance, a shape with 3 sides is referred to by the number '3', and a shape with 5 sides by '5'.
- As a variable 'n': In mathematical formulas or general discussions about polygons, the variable n is widely used to denote the number of sides. For example, the sum of interior angles of a polygon can be calculated using the formula (n-2) × 180°.
Naming Polygons by Their Side Count
Polygons are named by combining a Greek numerical prefix corresponding to their number of sides with the suffix "-gon." This systematic approach allows for clear identification of different polygon types.
Common Polygon Names
The table below illustrates common polygon names based on their number of sides:
| Number of Sides (n) | Polygon Name |
|---|---|
| 3 | Triangle (Trigon) |
| 4 | Quadrilateral (Tetragon) |
| 5 | Pentagon |
| 6 | Hexagon |
This naming pattern continues for polygons with more sides. For example, a polygon with 7 sides is a heptagon, 8 sides is an octagon, 9 sides is a nonagon, 10 sides is a decagon, and so forth, up to an icosagon for a 20-sided polygon.
