Chapter 2 of 8

All 8 chapters
  1. 1Straight lines and parallel lines, readunderstood
  2. 2Polygons, readunderstood
  3. 3Right angles and turns, readunderstood
  4. 4Measuring angles in degrees, readunderstood
  5. 5Triangles and four sided shapes, readunderstood
  6. 6Lines of symmetry, readunderstood
  7. 7Solid shapes and nets, readunderstood
  8. 8Grids and directions, readunderstood

M2.5.2 Chapter 2

Polygons

Is a circle a polygon?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Name shapes with 3 to 8 straight sides
  • Sort polygons by their sides and corners
  • Tell a regular polygon from one that is not regular

A polygon is a flat, closed shape with straight sides. Closed means there is no gap.

A circle is not a polygon. Its edge is curved.

Draw it first

Join straight sides to close a shape

  1. A row of polygons. Step 1 shows a triangle labelled 3 sides. Step 2 adds a shape labelled 4 sides. Step 3 adds a shape labelled 5 sides. Step 4 adds a shape labelled 6 sides.3 sides

    1 Join 3 straight lines so they close. You make a shape with 3 sides.

  2. A row of polygons. Step 1 shows a triangle labelled 3 sides. Step 2 adds a shape labelled 4 sides. Step 3 adds a shape labelled 5 sides. Step 4 adds a shape labelled 6 sides.3 sides4 sides

    2 Use 4 lines. Now the shape has 4 sides.

  3. A row of polygons. Step 1 shows a triangle labelled 3 sides. Step 2 adds a shape labelled 4 sides. Step 3 adds a shape labelled 5 sides. Step 4 adds a shape labelled 6 sides.3 sides4 sides5 sides

    3 Use 5 lines. The shape has 5 sides.

  4. A row of polygons. Step 1 shows a triangle labelled 3 sides. Step 2 adds a shape labelled 4 sides. Step 3 adds a shape labelled 5 sides. Step 4 adds a shape labelled 6 sides.3 sides4 sides5 sides6 sides

    4 Use 6 lines. The shape has 6 sides.

A shape with 4 sides is a quadrilateral. Every polygon is named by its sides.

Six polygons in two rows. The first row shows a triangle with 3 sides, a quadrilateral with 4 sides and a pentagon with 5 sides. The second row shows a hexagon with 6 sides, a heptagon with 7 sides and an octagon with 8 sides.triangle3 sidesquadrilateral4 sidespentagon5 sideshexagon6 sidesheptagon7 sidesoctagon8 sides
The names of polygons with 3 to 8 sides.

Count the corners too. A polygon has as many corners as sides.

See it three ways

With things

Lay 5 sticks end to end to make a closed shape. Count the sticks. Count the corners.

As a picture

A pentagon with a dot on each of its 5 corners. The label says 5 sides, 5 corners.5 sides, 5 corners

In symbols

Sides = corners. 5 sides, 5 corners.

Some polygons are regular. All their sides are equal. All their corners are the same size.

Two hexagons with a dot on each corner. The left one has six equal sides and six corners of the same size. It is labelled regular. The right one has sides of different lengths. It is labelled not regular.regularnot regular
Both shapes are hexagons. Only one is regular.

Equal sides are not enough. The corners must match too. Small ticks mark sides of equal length.

Three four sided shapes with small ticks on equal sides. A square has four equal sides. A rhombus has four equal sides but leans, so its corners are not all the same size. A rectangle has corners that are all the same size, but its sides are not all equal.squarerhombusrectangle
Only the square is regular. A square turned on its corner is still a square.

Try it

Make shapes from sticks

You need: 4 sticks of the same length, 2 more sticks, or strips of paper.

  1. Lay 4 sticks of the same length to make a square.
  2. Count the sides. Count the corners.
  3. Push one corner sideways so the shape leans.
  4. Look at the sides. They are all still equal.
  5. Look at the corners. They are no longer the same.
  6. Now use 6 sticks. Make a closed shape and name it.

What you will see: The sides stay equal, but the corners change. Equal sides alone do not make a regular shape.

If you cannot try it, this is what happens.
Two shapes made of four equal sticks. The left one is a square, labelled before. The right one has been pushed so it leans, labelled after. Ticks show that all four sides are equal in both.beforeafter

A wrong idea many people have

If all the sides are equal, the shape is regular.

Why it feels right: Equal sides look fair and even, so the shape seems regular.

The test that breaks it: Make a square with 4 equal sticks. Push it so it leans. The sides stay equal. The corners do not.

What is true: Regular needs equal sides and equal corners. Both must be true.

Key words

polygon
a flat, closed shape with straight sides.
quadrilateral
a polygon with 4 sides.
regular
all sides equal and all corners the same size.

Back to your guess

The answer is B: No. A polygon has only straight sides.

A polygon has straight sides only. A circle has a curved edge, so it is not a polygon.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

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

    Tap your answer.

    1. Not this one. A pentagon has 5 sides. You may have missed one side when you counted. Try another.

    2. Yes, that is right. A hexagon has 6 sides. A pentagon has 5. An octagon has 8.

    3. Not this one. An octagon has 8 sides. You may have mixed up two names. Try another.

    See the answer

    Hexagon

    A hexagon has 6 sides. A pentagon has 5. An octagon has 8.

    • If you chose A: A pentagon has 5 sides. You may have missed one side when you counted.
    • If you chose C: An octagon has 8 sides. You may have mixed up two names.

  2. How many sides does this polygon have? What is it called?

    A polygon with a dot on each of its 7 corners.
    See the answer

    7 sides, a heptagon

    Count the dots. There are 7 corners, so there are 7 sides. A polygon with 7 sides is a heptagon.

  3. Which of these is not a polygon?

    Tap your answer.

    1. Not this one. A triangle is closed with 3 straight sides. It is a polygon. Try another.

    2. Yes, that is right. A circle has a curved edge. A polygon has only straight sides.

    3. Not this one. A pentagon is closed with 5 straight sides. It is a polygon. Try another.

    See the answer

    A circle

    A circle has a curved edge. A polygon has only straight sides.

    • If you chose A: A triangle is closed with 3 straight sides. It is a polygon.
    • If you chose C: A pentagon is closed with 5 straight sides. It is a polygon.

  4. Which shape is a regular polygon?

    Three four sided shapes with ticks on equal sides. Shape A is a square. Shape B is a rhombus that leans. Shape C is a rectangle that is longer than it is tall.ABC
    Tap your answer.

    1. Yes, that is right. A has equal sides and equal corners. B has only equal sides. C has only equal corners.

    2. Not this one. Its sides are equal. Its corners are not all the same size. Try another.

    3. Not this one. Its corners match. Its sides are not all equal. Try another.

    See the answer

    Shape A

    A has equal sides and equal corners. B has only equal sides. C has only equal corners.

    • If you chose B: Its sides are equal. Its corners are not all the same size.
    • If you chose C: Its corners match. Its sides are not all equal.

  5. A regular octagon has 8 equal sides. Each side is 3 cm long. How far is it all the way round, in cm?

    See the answer

    24 cm

    8 sides of 3 cm each. 8 × 3 = 24 cm.

  6. From an earlier chapter

    A line runs from the 2 mark to the 9 mark. How long is it, in cm?

    A ruler marked from 0 to 9 with the word cm. A line runs from a cross above the 2 mark to a cross above the 9 mark.0123456789cm
    See the answer

    7 cm

    The line starts at 2, not at 0. From 2 to 9 is 9 − 2 = 7 cm.

  7. Which shape is a polygon?

    Three shapes. Shape A has straight sides, but there is a small gap between two of its ends. Shape B is a circle. Shape C is a pentagon with 5 straight sides.ABC
    Tap your answer.

    1. Not this one. Its sides are straight, but the shape has a gap. A polygon must be closed. Try another.

    2. Not this one. A circle is closed, but its edge is curved. A polygon has straight sides only. Try another.

    3. Yes, that is right. C is closed and has only straight sides. A has a gap, and B has a curved edge.

    See the answer

    Shape C

    C is closed and has only straight sides. A has a gap, and B has a curved edge.

    • If you chose A: Its sides are straight, but the shape has a gap. A polygon must be closed.
    • If you chose B: A circle is closed, but its edge is curved. A polygon has straight sides only.

  8. Ravi turns a square so that it stands on a corner. Is it still a square?

    A square turned so that it stands on one corner, labelled Ravi's shape. Small ticks mark that all four sides are equal. Small squares mark four right angles.Ravi's shape
    Tap your answer.

    1. Not this one. Turning moves the whole shape. Each side keeps its length. Each corner keeps its size. Try another.

    2. Yes, that is right. Turning does not change the sides or the corners. A square on its corner is still a square.

    3. Not this one. A square is named by 4 equal sides and 4 equal corners. How it sits does not matter. Try another.

    See the answer

    Yes. Turning a shape does not change its sides or corners.

    Turning does not change the sides or the corners. A square on its corner is still a square.

    • If you chose A: Turning moves the whole shape. Each side keeps its length. Each corner keeps its size.
    • If you chose C: A square is named by 4 equal sides and 4 equal corners. How it sits does not matter.

Keep it

Copy this into your exercise book.

A polygon is a flat, closed shape with straight sides. It has as many corners as sides. Regular means equal sides and equal corners.

Draw: A hexagon. Mark each corner with a dot and count them.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

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