Before we can understand what a polygon is, we must understand what it means for a shape to be closed.

If a shape is closed, you can take a pencil and trace it all the way around back to where you started, without running into any breaks. If there is a break in the shape, that means it is not closed and is called an open shape.

Let’s consider the following two shapes:

1) Oval

2) Hexagon that is missing one side

The first shape is closed because you can trace the oval all the way around, back to where you started without running into any breaks or openings.

The second shape, however, is open because there is a break in the line. This shape is not completely closed in.

What is a Polygon?

A polygon is a closed figure made up of line segments.

Below given are some examples of a Polygon:

1. Rectangle

2. Triangle

3. Regular hexagon (6 sides)

As you can see, not all polygons are regularly shaped. Some of them look quite odd.

In order to be a polygon, a shape must meet two requirements:

1. It must be closed.

2. It must be made up of line segments.

This means if there is any curve in the shape, it is not a polygon.

Here are few examples of shapes that are not polygons:

1. Circle

This circle is not a polygon because it is not made of line segments. Any shape that is curved is not a polygon.

2. An open square (square with one side missing)

This is not a polygon because it is not closed. One side is missing.

Let’s consider some more examples:

Determine whether each shape given below is a polygon or not.

1. Closed pentagon

Yes, this is a polygon because it is closed and it is made of line segments (no curves.)

2. Semicircle

No, this is not a polygon because it is not made of line segments. (It has a curve.)

The word “polygon” comes from the two Greek words: ‘Poly’ and ‘Gon’. ‘Poly’ means many and ‘gon’ means angles. Thus, a polygon has many angles.

# Summary

If a shape is closed, you can take a pencil and trace it all the way around, back to where you started without running into any breaks. If there is a break in the shape, that means it is not closed and is called an open shape.

A polygon is a closed figure made up of line segments.