National 5 Maths
Similar Shapes
Course content
- Similar figure questions involving length, area and volume scale factors
- Questions may include real-life contexts such as cost in proportion to area or volume.
Textbook page references
- Zeta National 5+ Maths
pp.199-206 - TeeJay Maths N5 Book 4+ pp.166-177
- Leckie National 5 Maths pp.238-248
Key ideas
- Mathematically similar shapes have equal angles, but one shape is an enlargement of the other.
- Linear scale factor (LSF or just SF) is the ratio of corresponding lengths.
- Area scale factor (ASF) is the ratio of areas. ASF = LSF2 so LSF \(= \sqrt{\small\textsf{ASF}}\normalsize\)
- Volume scale factor (VSF) is the ratio of volumes. VSF = LSF3 so LSF = \( \sqrt[\leftroot{-1}\uproot{3}\scriptstyle 3]{\small\textsf{VSF}\normalsize}\)
- We like to use \(\frac{\textsf{big}}{\textsf{small}}\) for an enlargement or \(\frac{\textsf{small}}{\textsf{big}}\) for a reduction, so that finding an unknown quantity always involves multiplying by the relevant scale factor. Both cases may also be remembered as \(\frac{\textsf{new}}{\textsf{old}}\small.\)
- Some teachers prefer to use \(\frac{\textsf{big}}{\textsf{small}}\) in both cases, but to divide for a reduction. Do what works best for you.
N5 Maths revision course
National5.com self-study courseSave £10 with discount code 'Maths.scot'
Example 1 (calculator)
Triangles ABC and DEF are mathematically similar. Find:
(a) length DF
(b) length BC
Example 2 (calculator)
An art supplies shop sells three mathematically similar picture frames. The following information is known:
| Size | Length | Price |
| Small | 20 cm | £4.80 |
| Medium | 30 cm | (a) |
| Large | (b) | £24.30 |
The frames are priced in direct proportion to their areas. Find:
(a) the price of the medium frame
(b) the length of the large frame.
Recommended student book
Zeta Maths: National 5 Maths Textbook
Best price, direct from the publisher
Example 3 (calculator)
A tinned food company sells two can sizes. The two cans are mathematically similar. The radii of the cans are 7 cm and 9 cm. The volume of the larger can is 1458 ml. What is the volume of the smaller can?
Example 4 (calculator)
Two rectangles have widths 12 cm and 20 cm. Their respective areas are 180 cm2 and 500 cm2. Are they mathematically similar? Justify your answer.
Example 5 (calculator)
SQA National 5 Maths 2014 P2 Q5
A supermarket sells cylindrical cookie jars which are mathematically similar.
The smaller jar has a height of 15 centimetres and a volume of 750 cubic centimetres.
The larger jar has a height of 24 centimetres.
Calculate the volume of the larger jar.
Recommended revision guides
How to Pass National 5 MathsBrightRED N5 Maths Study Guide
Example 6 (calculator)
SQA National 5 Maths 2015 P2 Q9
The flag at each hole on a golf course is coloured red and blue.
The diagram below represents a flag.
Triangle QRT represents the red section.
PQTS represents the blue section.
Triangles PRS and QRT are mathematically similar.
The area of triangle QRT is 400 square centimetres.
Calculate the area of PQTS, the blue section of the flag.
Example 7 (calculator)
SQA National 5 Maths 2017 Specimen P2 Q7
Screenwash is available in bottles which are mathematically similar.
The smaller bottle has a height of 15 centimetres and a volume of 250 millilitres.
The larger bottle has a height of 36 centimetres.
Calculate the volume of the larger bottle.
N5 Maths practice papers
Non-calculator papers and solutionsCalculator papers and solutions
Example 8 (calculator)
SQA National 5 Maths 2018 P2 Q18
A cinema sells popcorn in two different sized cartons.
The small carton is 16 centimetres deep and has a volume of 576 cubic centimetres.
The large carton is 24 centimetres deep and has a volume of 1125 cubic centimetres.
(a) Show that the two cartons are not mathematically similar.
The large carton is redesigned so that the two cartons are now mathematically similar.
The volume of the redesigned large carton is 1500 cubic centimetres.
(b) Calculate the depth of the redesigned large carton.
Example 9 (calculator)
SQA National 5 Maths 2021 P2 Q13
The two photographs shown are mathematically similar.
The small photograph has an area of 80 square centimetres, and is 12 centimetres wide.
The large photograph has an area of 500 square centimetres.
Calculate the width of the large photograph.
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Maths.scot worksheet
| • Similar shapes worksheet • Answer sheet • See all National 5 Maths worksheets |
Past paper questions
Other great resources
| Videos - Maths180.com |
| Videos - Larbert High School 1. Linear scale factor 2. Area and volume scale factors |
| Videos - Mr Graham Maths 1. Similar triangles 2. Area scale factors 3. Volume scale factors |
| PowerPoint - MathsRevision.com |
|
• Revision notes - BBC Bitesize • Test yourself - BBC Bitesize |
| Notes - D R Turnbull |
| Lesson notes - Maths 777 1. Linear scale factors 2. Area and volume scale factors 3. Finding the scale factor |
| Notes - Maths4Scotland.co.uk |
| Worked examples - Maths Mutt |
| Practice questions - Maths Hunter |
| Worksheet - Brannock HS Essential Skills 28 (Answers) |
| Exercises - Larkhall Academy Pages 32-56 Ex 1-8 (no answers) |
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