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Grade 10 areas of similar figures worksheets

HSG-SRT.B.5 Measurement and geometry

Printable areas of similar figures worksheets for grade 10, aligned to Common Core standard HSG-SRT.B.5. Area scales by the factor squared.

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Sample problems

  1. Two similar figures have a scale factor of 3. The smaller one has an area of 6 cm². What is the area of the larger one? 54 cm²
  2. Two similar figures have a scale factor of 4. The larger one has an area of 144 cm². What is the area of the smaller one? 9 cm²
  3. Two similar figures have a scale factor of 2. The smaller one has an area of 10 cm². What is the area of the larger one? 40 cm²
  4. Two similar figures have a scale factor of 4. The smaller one has an area of 3 cm². What is the area of the larger one? 48 cm²
  5. Two similar figures have a scale factor of 2. The larger one has an area of 36 cm². What is the area of the smaller one? 9 cm²
  6. Two similar figures have a scale factor of 4. The larger one has an area of 160 cm². What is the area of the smaller one? 10 cm²
  7. Two similar figures have a scale factor of 2. The smaller one has an area of 8 cm². What is the area of the larger one? 32 cm²
  8. Two similar figures have a scale factor of 3. The larger one has an area of 45 cm². What is the area of the smaller one? 5 cm²

These eight are one sample at medium difficulty — the generator makes a different set every time.

A worked example

Two similar figures have a scale factor of 3. The smaller one has an area of 6 cm². What is the area of the larger one? 54 cm²

  1. Lengths scale by 3, so area scales by 3² = 9
  2. 6 × 9 = 54 cm²

Every problem on the answer key can show its steps like this — turn on “Show steps” before downloading.

About these worksheets

Each problem states its own measurements, so the reasoning is the same but the arithmetic is new every time. Every sheet is generated fresh, so you can print a new one on the same skill as often as you need — different numbers, same difficulty.

Pick how many problems you want and whether they should be easy, medium or hard, then download a PDF with a matching answer key. The key can show the worked steps for every problem, which is what a parent needs to see where a wrong answer went wrong.

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