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      Identify and describe the relationship between irregular polygons using scale factors

      Lesson details

      Learning outcome

      You can identify and describe the relationship between two irregular polygons using scale factors

      Key learning points

      1. Two similar shapes can be described as being 'x' times greater or smaller than each other.
      2. If one similar shape is smaller than another, the scale factor is a fraction.
      3. Shapes related by a scale factor are similar.

      Keywords

      • Irregular polygon - An irregular polygon is a polygon where the sides and angles are not all equal

      Common misconception

      Not comparing the same or corresponding sides of related shapes.

      Label the sides of shapes clearly and refer to them with consistent language of height and width.

      Teacher tip

      Make sure that pupils have the opportunity to explain what is happening as the shapes are scaled and that all dimensions are being multiplied by the same scale factor.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      There is lots of information given about this shape. Which bits of information tell you about its dimensions?

      An image in a quiz
      Correct answer: Length of sides 6 cm
      Area is 36 squared cm
      Opposite sides are parallel
      Angles are right angles

      Q2.
      Which of these pairs of shapes are similar?

      An image in a quiz
      Correct answer: A
      B
      A and B
      Neither A or B

      Q3.
      What is the scale factor between hexagons A and B?

      An image in a quiz
      2
      3
      4
      Correct answer: 5
      8

      Q4.
      What number is one and a half times the size of 6?

      3
      6
      Correct answer: 9
      12

      Q5.
      Which of these shapes is similar to triangle A with a scale factor of 4?

      An image in a quiz
      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz

      Q6.
      Which of these shapes is similar to square A with a scale factor of one half?

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz

      6 Questions

      Q1.
      Which of these shapes are regular polygons?

      rectangle
      trapezium
      Correct answer: equilateral triangle
      right angled triange
      Correct answer: square

      Q2.
      Which of these shapes are irregular polygons

      Correct answer: rectangle
      Correct answer: trapezuim
      equilateral triangles
      Correct answer: right angled triangle
      square

      Q3.
      Is a hexagon a regular shape?

      Yes
      No
      Correct answer: Yes if all its sides are the same length

      Q4.
      A and B are similar rectangles. What is the missing dimension in rectangle B?

      An image in a quiz
      15 cm
      40 cm
      20 cm
      Correct answer: 30 cm

      Q5.
      This ratio table gives the dimensions of two rectangles. What is the scale factor between the rectangles?

      An image in a quiz
      2
      3
      4
      5
      Correct answer: 6

      Q6.
      What is the relationship between the height and width of both rectangles?

      An image in a quiz
      Correct answer: The ratio of height to width in both rectangles is 1 to 2 or 1 : 2
      Correct answer: The height of each rectangle is double the width
      Correct answer: The width of each rectangle is half the height

      To help you plan your 6 maths lesson on: Identify and describe the relationship between irregular polygons using scale factors, download all teaching resources for free and adapt to suit your pupils' needs...