Explanation
A polygon is a closed shape made of straight-line segments. Polygons can be classified in different ways according to their side lengths, angles, and structure.
The word polygon comes from Greek:
- Poly- means many
- -gon means angle
Therefore, a polygon is a closed shape with many angles.
Polygons are named based on the number of sides they have.
| Number of Sides | Name |
|---|---|
| 3 | Triangle |
| 4 | Quadrilateral |
| 5 | Pentagon |
| 6 | Hexagon |
| 7 | Heptagon |
| 8 | Octagon |
| 9 | Nonagon |
| 10 | Decagon |
Types of Polygons
Polygons can be classified in three different ways.
1. Regular and Irregular Polygons
A regular polygon has:
- All sides equal.
- All interior angles equal.
An irregular polygon has at least one side or angle different.
Examples
- Equilateral triangle → Regular
- Square → Regular
- Rectangle → Irregular
- Scalene triangle → Irregular
2. Convex and Concave Polygons
A convex polygon has all interior angles less than \(180^\circ\).
A concave polygon has at least one interior angle greater than \(180^\circ\).
Examples
- Triangle → Convex
- Rhombus → Convex
- Arrow-shaped pentagon → Concave
Concave or Convex Polygon Test
A simple test to determine whether a polygon is convex or concave is to draw a line segment between any two points inside the polygon.
- If the entire line segment stays inside the polygon, the polygon is convex.
- If part of the line segment goes outside the polygon, the polygon is concave.
3. Simple and Complex Polygons
A simple polygon has sides that do not cross each other.
A complex polygon (also called a self-intersecting polygon) has sides that intersect or cross each other.
Examples
- Triangle → Simple polygon.
- Pentagon → Simple polygon.
- Five-pointed star → Complex polygon.
Formula / Rule
Regular Polygon
All sides equal and all angles equal.
Irregular Polygon
At least one side or angle is different.
Convex Polygon
All interior angles are less than \(180^\circ\).
Concave Polygon
At least one interior angle is greater than \(180^\circ\).
Simple Polygon
Sides do not intersect.
Complex Polygon
Sides intersect (self-intersecting).
Example
Example 1
Classify the following polygon.
A square with four equal sides and four right angles.
Solution
All sides are equal and all angles are equal.
Therefore, the square is a regular polygon.
It is also:
Video Explanation
Practice
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- Polygons (Basics)
- Types of Polygons (Current lesson)
- Is this a Polygon