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Similar shapes have the same shape but different size, related by a scale factor. This topic finds missing lengths and uses the area and volume scale factors (k² and k³). It's a core topic in GCSE and iGCSE Maths with Edexcel and the other major boards. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Match up corresponding sides and divide to find the length scale factor. Square it for areas and cube it for volumes. Always check which shape is the larger before you multiply or divide.
Before you start
Before starting, revisit ratio and scale factors. You will lean on this again for area and volume scale factors, and trigonometry.
What you learn
That ratio is the length scale factor. Crucially, areas scale by the factor squared and volumes by the factor cubed. Similar shapes have equal angles and corresponding sides in the same ratio. For solids, when lengths scale by k, volumes scale by k³. The course works through similar shapes and length scale factor, area scale factor and volume scale factor. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our GCSE maths courses, Similar Shapes belongs to Ratio and Proportion and is met in Higher tier. You work through 3 concepts and 2 worked examples, testing yourself at 3 points. Related topics students usually take next include Speed, Distance, Time, Unit Conversion, Compound Measures and Density & Pressure. The Ratio and Proportion revision engine gives you as many extra questions as you want, tracked on your skill tree.
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