Types Of Polygon

The concept of types of polygon plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Knowing polygon types helps students in geometry questions, visual recognition, reasoning, and more. Let’s explore all main types of polygons: their definitions, properties, classification, and tricks to remember them for exams and everyday problem-solving.

What Is Types of Polygon?

A polygon is defined as a closed, flat, two-dimensional (2D) shape consisting of straight, non-intersecting line segments called sides. These sides join each other at points called vertices. In mathematics, polygons are often classified by the number of sides/angles and how those sides/angles are measured. You’ll find this concept applied in geometry, reasoning, and many competitive exams.

Classification of Polygons (Based on Sides)

Polygons are named and classified according to the number of sides they have. Here’s a handy table for quick reference:

No. of Sides	Polygon Name	Example Image
3	Triangle	▲
4	Quadrilateral	■
5	Pentagon	⬟
6	Hexagon	⬢
7	Heptagon	-
8	Octagon	⯃
9	Nonagon	-
10	Decagon	-
11	Hendecagon	-
12	Dodecagon	-
n	n-gon	-

Types of Polygon in Maths

Polygons can also be classified based on the lengths of sides, the measurement of angles, and the overall arrangement of their sides/angles. These subtypes help solve various “classification of polygons” questions in exams as well as visual reasoning puzzles. The key types of polygon are:

• Regular Polygon: All sides and angles are equal (e.g., square, equilateral triangle, regular hexagon).
• Irregular Polygon: Sides or angles are unequal (e.g., scalene triangle or non-square rectangles).
• Convex Polygon: All interior angles < 180°, and no vertex points inward.
• Concave Polygon: At least one interior angle > 180°, at least one vertex points inward.
• Simple Polygon: Sides do not cross each other (standard polygons).
• Complex Polygon: Sides cross each other (self-intersecting shapes).

Key Formula for Types of Polygon

Here are some essential formulas related to all types of polygons:

• Sum of Interior Angles: \( (n - 2) \times 180^\circ \), where n = number of sides
• Each Interior Angle (Regular Polygon): \( \frac{(n - 2) \times 180^\circ}{n} \)
• Number of Diagonals: \( \frac{n(n - 3)}{2} \)
• Sum of Exterior Angles: Always 360°

Regular vs. Irregular, Convex vs. Concave — With Examples

Type	Features	Example
Regular Polygon	All sides/angles equal	Equilateral Triangle, Square
Irregular Polygon	Sides/angles unequal	Scalene Triangle, Rectangle (not square)
Convex Polygon	No angle > 180°, vertices point outward	Regular Pentagon
Concave Polygon	At least one angle > 180°, one vertex inward	Star shape

How to Identify Polygon Types Quickly

• If all sides/angles are equal → Regular Polygon
• If any side/angle differs → Irregular Polygon
• If all angles < 180° → Convex Polygon
• If any angle > 180° → Concave Polygon

Trick: If you can draw a line between any two points inside the shape and it never leaves the shape, it’s convex; else it’s concave. This tip is used in polygon classification MCQs in most exams.

Common Properties of All Types of Polygon

• The number of vertices = number of sides
• Polygon is always closed
• Sides are straight (never curved)
• The sum of all exterior angles for any polygon = 360°
• The sum of all interior angles = (n – 2) × 180°

Practical Examples & Real-life Usage

• Triangle (3 sides): Traffic signs, pyramids
• Pentagon (5 sides): The Pentagon building (USA)
• Hexagon (6 sides): Honeycombs
• Octagon (8 sides): Stop signs
• Quadrilateral (4 sides): Windows, books, tiles

Step-by-Step Illustration

1. Find the sum of angles in a hexagon. n = 6 Using formula: (n – 2) × 180° = (6 – 2) × 180° = 4 × 180° = 720°
2. What is the interior angle of a regular octagon? n = 8 Each angle = (8 – 2) × 180° / 8 = 6 × 180° / 8 = 1080° / 8 = 135°

Speed Trick or Vedic Shortcut

To quickly remember polygon names: “TQPHHONDID” = Triangle, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, etc. Just count up from 3 and recall this order for MCQs!

For fast angle sum: Subtract 2 from the number of sides, multiply by 180°. Example: 7 sides → (7 – 2) × 180° = 5 × 180° = 900°.

Try These Yourself

• Write the names of polygons with 3 to 8 sides.
• Check if a given shape with one inward vertex is concave or convex.
• Calculate the sum of all angles for a decagon.
• Decide which of these is a regular polygon: rectangle, equilateral triangle, parallelogram, square.

Frequent Errors and Misunderstandings

• Assuming circles or ovals are polygons (they MUST have straight sides).
• Mixing up sides with vertices.
• Forgetting to use (n – 2) × 180° for TOTAL interior angle sums.
• Identifying rectangles as regular polygons (only square is regular, rectangle is irregular).

Relation to Other Concepts

The idea of types of polygon connects closely with regular polygons, area of a polygon, as well as concepts like perimeter, diagonal formula, and angle types. Mastering this helps in advanced geometry, mensuration, and reasoning in math competitions.

Classroom Tip

A quick way to recall polygon types: Use your hand—start with a triangle (3), add a finger each time for quadrilateral, pentagon, etc. This helps you visually and physically count sides and connect their names. Vedantu’s teachers use such tricks in live classes for smart visual learning!

Recommended Internal Links

• Regular Polygon: Full Geometry Notes
• Convex Polygon: Definition & Properties
• Area of a Polygon: Formulas & Examples
• Types of Angles: Interactive Guide

We explored types of polygon—from definitions, properties, types, mistakes to avoid and neat classroom tricks for memorization. Keep practicing with Vedantu to master polygon types and boost your confidence in geometry questions for board and competitive exams!