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# Polygons – Explanation & Examples

Have you heard about a polygon? Well, **polygons are all around us!** Most of the common shapes that you see or study every day are polygons. You see a wall, which is rectangular in shape, is a polygon.

A front view of a dice, which has a square shape, is a polygon. A pizza slice is triangular in shape, hence, a polygon.

**In this article, you will learn:**

- What polygons are, and how do they look like.
- The different types of polygons.

## What is a Polygon?

**In mathematics, a polygon is a closed two-dimensional figure made up of line segments but not curves. The term polygon originates from the Greek word “poly -” meaning “many” and “- gon,” meaning “angles.” **

The most common examples of polygons are the triangle, the rectangle, and the square. In simple words, polygons are plain figures or shapes made up of line segments only.

**Note:** Circles, three-dimensional objects, any shapes that include curves, and any shapes that aren’t closed are not polygons.

Polygons were known to human beings since ancient times. **Greeks studied non-convex regular polygon in 7 ^{th} century BC** on a krater by Aristophanes. Thomas Bradwardine was the first known person to study non-convex polygons in the 14

^{th}century. The concept of polygons was generalized in 1952 by Geoffrey Colin.

Now that you have understood what a polygon is let us explore the different polygons and how they look.

## Types of Polygons

Depending on the sides and angles, the **polygons are classified into** different types, namely,

- Regular Polygon
- Irregular Polygon
- Convex Polygon
- Concave polygon

### Regular Polygon

A regular polygon is a polygon in which all the interior angles are equal, and also, all the sides are equal. There are different types of regular polygons.

*These are:*

**A triangle**: An equilateral triangle is a regular polygon with three equal side lengths and three equal angles.

**A quadrilateral.**A quadrilateral is a regular polygon with four angles and four sides. Examples of quadrilaterals are:

a. *A square*: A quadrilateral whose 4 sides are equal and four angles are all 90 degrees each.

b. *A rectangle:*

c. *Parallelogram*: Opposite sides are parallel, opposite sides are equal in length, opposite angles are equal

d. *Kite*: Two pairs of adjacent sides are of equal length; the shape has an axis of symmetry.

e. *Rhombus*: A special type of parallelogram in which all four sides are the same length, like a square that has been squashed sideways.

**Pentagon**: A polygon that has 5 equal sides and angle

**Hexagon:**A regular polygon that has 6 equal sides and 6 equal angles.

**Heptagon:**A regular polygon with 7 equal side lengths and 7 same angles.

**Octagon:**An octagon has 8 equal sides and 8 equal angles. The best real-life example of an octagon is the STOP road sign.

**Nonagon:**Has 9 equal sides and 9 same angles.

**Hendecagon:**Has 11 equal sides and 11 equal angles.**Dodecagon: a**regular polygon with 12 equal sides and 12 same angles**Triskaidecagon:**Has 13 equal sides and 13 same angles.**Tetrakaidecagon**: Has 14 equal sides and 14 same angles.**Pentadecagon:**A pentadecagon is a regular polygon with 15 equal sides and 15 same angles.**Hexakaidecagon**: has 16 sides and angles.**Heptadecagon**: Has 17 sides and angles.**Octakaidecagon:**Has 18 sides and angles**Enneadecagon:**19 sides and 19 angles.**Icosagon:**Has equal sides and 20 equal angles**Hectagon:**Has 100 equal sides and 100 equal angles.**Chiliagon:**Has 1000 sides**Myriagon:**10000 sides.**Megagon:**One million sides.**n-gon**: Has n- equal sides.

### Irregular polygon

An irregular polygon is a polygon with a different measure of angles and side lengths.

*Examples of irregular polygons:*

### Convex Polygon

This is a type of polygon with all the interior angles strictly less than 180 degrees. The vertex of a convex polygon always points outwards from the center of the shape.

### Concave Polygon

If one or more interior angles of a polygon are more than 180 degrees, it is known as a concave polygon. A concave polygon can have at least four sides—the vertex points towards the inside of the polygon.

The following are a few mnemonics to help remember the names of some polygons:

- A QuadBike has 4 wheels and thus a quadrilateral.
- The Washington DC in the US has 5 sides (Pentagon).
- A
**H**oneycomb has 6 sides (**H**exagon). **S**eptagon has 7 sides (**S**even).- An Octopus has 8 tentacles (octagon).
- The terms
**N**onagon and**N**ine both start with the letter N. - A
**Decagon**has 10 sides, just like a**D**ecimal point has 10 digits.

### Real-life applications of polygons

Understanding shapes is important in geometry. Shapes have a wide application in real-life applications.

*For example:*

- The tiles that you walk on are squared in shape, which implies that they are polygons.
- The truss of a building or bridge, the walls of a building, etc., are examples of polygons. Trusses are triangular in shape, while walls are rectangular shaped.
- The rectangular part of a chair on which you are sitting is an example of a polygon.
- The rectangular-shaped screen of your laptop, television, or mobile phone is an example of a polygon.
- A rectangular football pitch or playground is an example of a polygon.
- The Bermuda Triangle, which is a triangular shape, is a polygon.
- The Pyramids of Egypt are also an example of polygons (triangular)
- Star-shaped figures are examples of a polygon.
- Road signs are also an example of polygons.

*Example*

John has a rectangular piece of paper. He wants to cut the paper so that he gets two more polygons (other than a rectangle) of the same size and shape. Suggest the possible ways.

__Solution__

There are two possible ways to cut a rectangular piece of paper in such a way that he gets two more polygons (other than a rectangle) of the same size and shape:

- He can cut a rectangular piece of paper exactly from the center vertically to get the two squares of the same size and shape.
- He can cut a rectangular piece of paper diagonally to get the two triangles of the same size and shape.

*Practice Questions*

*Practice Questions*

Guess the polygon:

- I am a plane figure with 4 sides of equal lengths and 90-degree angles on the sides.
- I am a plane figure with 2 sides, each of equal length and 90-degree angles on the sides.
- I am a plane figure with 6 sides, and all interior angles are greater than 90 degrees.

__Answers__

- Square
- Rectangle
- Hexagon