Standard 3 Maths

Polygons: Regular, Irregular and Turned Shapes – Standard 3 Maths

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What you will learn

  • Name polygons by their number of sides: triangle, quadrilateral, pentagon, hexagon and octagon.
  • Tell regular polygons from irregular polygons.
  • Show that turning a shape does not change its shape or size, and solve problems with polygons.

Look at a stop sign on the way to school. Count its sides: 8. A stop sign is an octagon. In this lesson you will learn to name flat shapes by their sides, tell regular shapes from irregular ones and find out what happens when you turn a shape.

A red stop sign shaped like an octagon
A stop sign is a regular octagon: 8 sides of the same length. Photo: Novoklimov, CC0, via Wikimedia Commons.

What is a polygon?

A polygon is a flat, closed shape with straight sides. The corners are called vertices. A polygon has the same number of vertices as sides.

a polygon: 5 straight sides, closed

not a polygon: a circle is curved

not a polygon: it is not closed

not a polygon: one side is curved

Naming polygons

Polygons are named by how many sides they have.

triangle
3 sides, 3 vertices

quadrilateral
4 sides, 4 vertices

pentagon
5 sides, 5 vertices

hexagon
6 sides, 6 vertices

octagon
8 sides, 8 vertices

Honey bees on a honeycomb made of many hexagon cells
Bees build honeycomb from hexagons. Each cell has 6 sides. Photo: Axel Hindemith, public domain, via Wikimedia Commons.

Worked example 1

A shape has 6 straight sides. What is it called?

Show me how

Count the sides: 6.

A polygon with 6 sides is a hexagon.

It is a hexagon. It also has 6 vertices.

Regular and irregular polygons

A regular polygon has all its sides the same length and all its corners the same size. An irregular polygon does not. A square is a regular quadrilateral. A rectangle is an irregular quadrilateral, because its long sides and short sides are different.

regular triangle

irregular triangle

square: regular

rectangle: irregular

irregular quadrilateral

irregular hexagon

Worked example 2

Is a rectangle with sides 10 cm, 4 cm, 10 cm and 4 cm a regular polygon?

Show me how

A regular polygon needs all sides the same length.

Here 10 cm and 4 cm are different.

No. It is an irregular quadrilateral.

Turning shapes

Measure the sides of a shape. Then turn it and measure again. The sides are still the same length and the corners are still the same size. Turning a shape does not change its shape or its size. Only the way it faces changes.

a square

the same square, turned

a triangle

the same triangle, turned

Watch out! A common mistake

A square turned on its corner is often called a diamond, but it is still a square. Its 4 sides are still the same length and its corners are still square corners.

Worked example 3

Tariq cut out a pentagon. He measured each side: 3 cm. He turned it upside down. How long is each side now?

Show me how

Turning does not change the size of a shape.

The sides were 3 cm before turning.

Each side is still 3 cm.

Polygon problems

You can use what you know about sides to solve problems.

Worked example 4

Each side of a stop sign is 25 cm long. How far is it all the way around the sign?

Show me how

A stop sign is a regular octagon, so it has 8 sides of the same length.

8 × 25 cm = 200 cm.

It is 200 cm all the way around.

To count the sides of several shapes, add: 2 triangles and 1 hexagon have 3 + 3 + 6 = 12 sides.

Try it

TRY ITPolygon pro

Name polygons, count sides, sort regular from irregular, check turned shapes and solve polygon problems.

Let’s practise

Work out each one in your copybook. Open Hint if you are stuck, then open Show answer to check your working.

1. How many sides does a hexagon have?

Hint

Think of a honeycomb cell.

Show answer

6 sides

2. What is a polygon with 8 sides called?

Hint

Think of a stop sign.

Show answer

An octagon

3. Is a rectangle a quadrilateral?

Hint

Count its sides.

Show answer

Yes. It has 4 sides, so it is a quadrilateral.

4. Is a circle a polygon? Explain.

Hint

Does it have straight sides?

Show answer

No. A circle is curved and has no straight sides.

5. A square is turned so that it stands on a corner. Is it still a square?

Hint

Measure, turn, measure again.

Show answer

Yes. Its sides are still the same length and its corners still the same size.

6. What makes a polygon regular?

Hint

Think about sides and corners.

Show answer

All sides are the same length and all corners are the same size.

7. Draw a quadrilateral that is irregular. What could it be?

Hint

A long box shape.

Show answer

For example, a long rectangle, which has 2 long sides and 2 short sides.

8. Jada made 2 triangles and 1 hexagon with lollipop sticks, one stick for each side. How many sticks did she use?

Hint

Add the sides of each shape.

Show answer

3 + 3 + 6 = 12 sticks

Quiz

Lesson quiz: 10 questions

Answer every question, then press Check my answers. Score 8 or more to earn the Polygon Pro badge.

Recap

  • A polygon is a flat, closed shape with straight sides.
  • Triangle 3 sides, quadrilateral 4, pentagon 5, hexagon 6, octagon 8.
  • A polygon has the same number of vertices as sides.
  • Regular: all sides the same length and all corners the same size. Irregular: not.
  • Turning a shape does not change its shape or size.

Words to know

polygon
A flat, closed shape with straight sides.
Example: A hexagon is a polygon.
side
One of the straight lines of a polygon.
Example: A triangle has 3 sides.
vertex (vertices)
A corner of a polygon.
Example: A square has 4 vertices.
quadrilateral
A polygon with 4 sides.
Example: Squares and rectangles are quadrilaterals.
regular polygon
A polygon with all sides and all corners the same.
Example: A stop sign is a regular octagon.
irregular polygon
A polygon whose sides or corners are not all the same.
Example: A rectangle is irregular.

Try it at home

  • Look for polygons around your home and street: windows, floor tiles, a stop sign, a kite for Easter. Draw five of them and name each one.
  • Mini project: cut out a paper shape, measure its sides with a ruler, then turn it three different ways and measure again. Write what you notice.

Test tips

Tips for class tests

  • Count the sides carefully. Put a small tick on each side as you count it.
  • To decide if a shape is regular, check the sides and the corners.
  • A turned shape is the same shape. Do not let a “diamond” trick you.

For parents and teachers

After this lesson, your child should be able to:

  • recognise and name triangles, quadrilaterals, pentagons, hexagons and octagons;
  • distinguish between regular and irregular polygons;
  • investigate the effect of orientation on shape and size (measure, turn, measure again) and solve problems.

A helpful activity is to cut a shape from a cereal box, trace it, turn it and trace it again. Children see that the two tracings are the same shape and size, even though they face different ways.

Quiz scores and badges are saved only in this browser on this device. Nothing is sent anywhere. If the browser data is cleared, or another device is used, the badges will be lost.

Previous: Solids: Faces, Edges and Vertices – Standard 3 Maths
Next: Line Symmetry – Standard 3 Maths
Course: Standard 3 Maths

Updates

2026/11/06
– Linked the next lesson, Line Symmetry.

2026/11/05
– First version of this lesson.

Attributions to media used in this post:

Red octagonal stop sign.jpg – Novoklimov – CC0 1.0 (via Wikimedia Commons)

Bienen auf Honigwabe.jpg – Axel Hindemith – Public domain (via Wikimedia Commons)

© 2026 Vedesh Kungebeharry. All rights reserved.

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