Polygons and Their Types

A polygon is a closed, two-dimensional geometric figure made up of straight line segments. The line segments are called sides, and the points where two sides meet are called vertices.

Types of Polygons

Polygons are classified based on the number of sides, shape, and properties.

1. Based on the Number of Sides

2. Based on Shape

• Regular Polygon: All sides and angles are equal.
  • Example: Equilateral Triangle, Square.
• Irregular Polygon: Sides and angles are not equal.
  • Example: Scalene Triangle, Random Quadrilateral.

3. Based on Angle Properties

• Convex Polygon: All interior angles are less than 180° and vertices point outward.
  • Example: Regular Hexagon.
• Concave Polygon: At least one interior angle is greater than 180° and at least one vertex points inward.
  • Example: Star-shaped figure.

4. Based on Complexity

• Simple Polygon: Does not intersect itself.
  • Example: Triangle, Rectangle.
• Complex (Self-intersecting) Polygon: Has sides that cross each other.
  • Example: Star Polygon.

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How to Identify Whether a Given Shape is a Polygon or Not

A polygon is a closed figure made of straight line segments. To determine whether a given shape is a polygon, check the following conditions:

✅ It is a Polygon if:

1. It is a closed shape (no gaps).
2. It consists only of straight line segments (no curves).
3. The sides meet only at endpoints (no crossings or intersections).
4. It has at least three sides (minimum is a triangle).

All the conditions stated above for a shape to be a polygon must be met simultaneously. If even one condition is violated, the shape is not a polygon.

❌ It is NOT a Polygon if:

1. It has curved sides (e.g., circles, ovals, semicircles).
2. It is open (not a fully enclosed figure).
3. It has sides that cross each other (except for self-intersecting polygons).

Examples