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Grade 9 · Math · Unit 9 of 9

Similarity & Scale

Scale factors and similar figures

What your child practises

Using scale factors to find missing sides, solving shadow and scale-drawing problems, and seeing how enlarging a shape changes its area and volume.

Prince Edward Island Curriculum curriculum outcome: 9.SS3; 9.SS4 · similar triangles, scale factors and scale diagrams

How we explain it

Children can open this short lesson before they practise.

  1. Similar shapes have the same shape but different sizes.
  2. The scale factor is new length ÷ old length.
  3. Multiply every length by the scale factor. Areas change by the factor squared.

Example: A rectangle 4 cm by 6 cm is enlarged by a scale factor of 3. What are the new sides? 4 × 3 = 12. 6 × 3 = 18. Answer: 12 cm by 18 cm

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Triangle B is an enlargement of triangle A. A side of 2 cm on triangle A matches a side of 6 cm on triangle B. What is the scale factor?

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  2. Question 2

    Two rectangles are similar. The small one is 4 cm by 2 cm. The large one is 8 cm long. How wide is the large rectangle?

    answer boxcm

  3. Question 3

    △ABC ~ △DEF. AB = 3 cm, BC = 9 cm and DE = 6 cm. How long is EF?

    answer boxcm

  4. Question 4

    A 1 m stick casts a 2 m shadow. At the same time, a tree casts a 16 m shadow. How tall is the tree?

    answer boxm

  5. Question 5

    A scale drawing uses 1 cm for every 5 cm in real life. A wall measures 10 cm on the drawing. How long is the real wall in centimetres?

    answer boxcm

  6. Question 6

    A cube is enlarged by a scale factor of 3. By what factor does its volume grow?

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