How to Find the Number of Sides of a Polygon?
The concept of side of a polygon plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding sides helps you name polygons, compute perimeters, find interior and exterior angles, and classify shapes in geometry. Let’s dive into simple explanations, formulas, and examples to make this topic super clear!
What Is Side of a Polygon?
A side of a polygon is any straight line segment that forms part of the boundary of a polygon. In other words, it’s one of the straight edges with which the polygon is formed. Each side joins two adjacent vertices. You’ll find this concept applied in naming polygons (like triangle, pentagon, hexagon), calculating perimeters and areas, and in solving many geometry questions.
Key Formula for Side of a Polygon
Here’s an important formula you should know:
To find the number of sides (n) of a regular polygon from its exterior angle:
n = 360° ÷ Exterior Angle
Or, if the polygon’s interior angle (A°) is known:
n = 360° ÷ (180° − A°)
Cross-Disciplinary Usage
The side of a polygon is not only useful in Maths but also plays an important role in Physics, Computer Science, and daily logical reasoning. For example, it helps in calculating the path of robots (hexagonal or octagonal grids), in architectural designs, and in coding (for drawing shapes and designing games or puzzles). Students preparing for competitive exams like JEE, Olympiads, or NTSE will see this topic show up quite frequently.
Step-by-Step Illustration
- Suppose you’re told the exterior angle of a regular polygon is 45°. How many sides does it have?
Use the formula: n = 360° ÷ Exterior Angle = 360° ÷ 45° = 8.
So the polygon is an octagon (8-sided).
- If you know the interior angle is 120°, find the sides:
First, calculate the exterior angle = 180° – 120° = 60°.
Now, n = 360° ÷ 60° = 6.
So, it’s a hexagon (6-sided).
Table: Names of Polygons and Number of Sides
| Polygon Name | Number of Sides |
|---|---|
| Triangle | 3 |
| Quadrilateral (Square/Rectangle) | 4 |
| Pentagon | 5 |
| Hexagon | 6 |
| Heptagon | 7 |
| Octagon | 8 |
| Nonagon | 9 |
| Decagon | 10 |
| Dodecagon | 12 |
| Icosagon | 20 |
Regular vs. Irregular Sides in Polygons
| Regular Polygon | Irregular Polygon |
|---|---|
| All sides and angles are equal | Sides or angles are NOT equal |
| Example: Equilateral triangle, square | Example: Scalene triangle, general quadrilateral |
Speed Trick or Vedic Shortcut
Here’s a quick shortcut: If you forget the side formula, just remember that all exterior angles around a point add to 360°. So, number of sides = 360° / exterior angle—quickly done on your fingers in timed MCQs. In regular polygons, dividing 360° by the angle always works!
Example: If the exterior angle is 30°, then
360 ÷ 30 = 12 sides (so, dodecagon).
Vedantu’s online classes share neat memory tricks for formulas like this to help students ace their tests.
Try These Yourself
- What is the name of a 7-sided polygon?
- If the interior angle of a regular polygon is 150°, how many sides does it have?
- Is a kite a regular or irregular polygon?
- List all polygons you see at home (for example, a rectangular table, a stop sign, etc.)
Frequent Errors and Misunderstandings
- Using the interior angle directly in the formula instead of subtracting from 180° first.
- Mixing up sides and vertices—a side connects two vertices, but they aren’t the same thing.
- Assuming all polygons are regular without checking that all sides and angles are equal.
Relation to Other Concepts
The idea of the side of a polygon connects closely with types of polygons, regular polygons, and polygon angles. Mastering sides helps you calculate perimeters, areas, and understand more advanced geometry topics in higher classes.
Classroom Tip
A quick way to remember the names: “Tri–Quad–Pent–Hex–Hept–Oct–Non–Dec” means 3 to 10 sides in Greek/Latin prefixes! Repeat these names aloud to memorize them for life. Vedantu’s teachers use such fun drill techniques in live maths classes so you never forget polygons and their sides.
We explored side of a polygon—from its definition, easy formulas, examples, error checks, and ties to other geometric ideas. Continue practicing on Vedantu for even more tricks and quizzes on polygons and become a pro at spotting and solving polygons in no time!
Recommended Next:
