# Shapes: Polygons

## Introduction

There are many different shapes. There might seem to be hundreds of different shapes and you could try to learn them all but

• This is confusing

• This is a waste of time

• This is pointless. We need to see what they have in common and what is different about them.

It is much better to concentrate on the properties of shapes. This way you can remember a few facts and then use them to find out more about different shapes.

# Properties of shapes.

The 3 properties of shapes that we are going to look at are:

1. The number of sides

2. The interior angles (the angles inside).

3. The length of the sides.

These properties help us to remember which shapes are which and why they are so called (in some cases).

Let us look at shapes that have different numbers of straight sides.

Polygons ALWAYS have straight sides.

Here are the polygons you are expected to know about.

• Pentagon

• Hexagon

• Heptagon

• Octagon

That does not seem too many does it? Let us look at the properties of polygons.

Pentagon

A pentagon has got 5 sides. A regular pentagon has got 5 sides of equal length

The interior angles of a pentagon add up to 540°

Each interior angle of a regular pentagon measures 108°.

Both these shapes are pentagons; the first is a regular pentagon. Why is the other one a pentagon?

The answer is because it has got 5 sides!

The Americans have a building called the pentagon because of its shape.

Let us look at another polygon:

Hexagon

A hexagon has got 6 sides. A regular hexagon has got 6 sides of equal length

The interior angles of a hexagon add up to 720°

Each interior angle of a regular pentagon measures 120°. Can you think of a simple way to remember how many sides a hexagon as?

The answer is in the number six. They both have an X in them, six and hexagon

We are half way through now. What about another polygon?

Heptagon

The heptagon has got 7 sides. A regular heptagon has got 7 sides of equal length. Can you name two coins that are heptagons?

Both the 20p and the 50p coins are heptagons. Take a look at them.

Well it is time to meet the final polygon that we will cover today

Octagon

An octagon has got 8 sides. A regular octagon has got 8 sides of equal length.

The interior angles of an octagon add up to 1080°

Each interior angle of a regular pentagon measures 135°. Can you name an animal that will help you to remember the number of sides in an octagon?

An octopus. It has got eight tentacles.

Well those are the polygons that you must know? There are others but concentrate on these for the time being. Lets review what we have found out so far.

Review

Polygon means many sides.

All polygons have straight sides.

Polygons can be regular or irregular. (It is not the shape that matters but the number of straight sides).

The interior angles of polygons add up to different totals.

You need to remember these:

 Name Number of sides Interior angles Pentagon 5 108° Hexagon 6 120° Octagon 8 135°

Well that was not too bad. I hope that you remember all the facts. Good luck.