GCSE Maths (Edexcel)

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Similarity & Area

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Geometry and Measures Mensuration and Calculation

Similarity & Area

4:16 Similarity Calculations
Spec R12 G19
Previous Similarity & Perimeter Next Similarity & Surface Area
  • Similar shapes with a length ratio of 1 to n have an area ratio of 1 to n squared
  • Two shapes are similar if one is a larger or smaller version of the other
  • The smaller rectangle has side lengths of X and Y, while the larger rectangle has side lengths of 2X and 2Y
  • The length ratio in this example is 1 to 2, so n is equal to 2
  • The area ratio is 1 to 4 (2 squared)
  • The area of a rectangle is found by multiplying its width by its length
  • The area of the smaller rectangle is XY, and the area of the larger rectangle is 4XY
  • This relationship applies to all shapes, not just rectangles
  • In an example, the smaller shape has an area of 27 cm squared
  • The length ratio is 1 to 3, so the area ratio is 1 to 9
  • The area of the larger shape is found by multiplying the area of the smaller shape by the scale factor for the area (27 cm squared * 9 = 243 cm squared)

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