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Similar shapes
AQA GCSE Mathematics practice questions with step-by-step solutions
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Sample Questions
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EasyQuestion 1
[2 marks]Two similar triangles have sides 6 cm, 8 cm, 10 cm and 9 cm, 12 cm, 15 cm.
Find the scale factor from the smaller to the larger triangle.
Solution for Question 1
MediumQuestion 2
[3 marks]Two similar rectangles have areas 32 cm² and 72 cm².
The smaller rectangle has length 8 cm.
Find the length of the larger rectangle.
Solution for Question 2
HardQuestion 3
[4 marks]Two similar cones have volumes 250 cm³ and 2000 cm³.
The smaller cone has surface area 150 cm².
Find the surface area of the larger cone.
Solution for Question 3
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Similar shapes have the same shape but different sizes - all corresponding angles are equal and corresponding sides are in the same ratio (the scale factor). To prove similarity, show all angles match or all sides are in proportion.
The scale factor relationships are crucial: if the linear scale factor is k, then areas scale by k² and volumes scale by k³. So if a shape is enlarged by scale factor 3, its area is 9 times bigger and its volume (if 3D) is 27 times bigger.
To find missing lengths in similar shapes, first identify corresponding sides and find the scale factor, then multiply or divide appropriately.
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