Area scale factors
Objective. Connect area scale factor to the square of the linear factor.
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- 2. Worked example
- 3. Practice
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Learn: the key idea
The area scale factor between two similar shapes equals the square of the linear scale factor, because area depends on two dimensions multiplied together. If the linear scale factor between two similar shapes is k, then any corresponding areas are related by a factor of k². For example, if a small shape is enlarged with a linear scale factor of 3, its area becomes 3² = 9 times larger. This relationship works in reverse too: to find the linear scale factor from a known area scale factor, take the square root of the area ratio.
Worked example
Two similar polygons have a linear scale factor of 4. If the smaller polygon has an area of 12 cm², find the area of the larger polygon.
- 1The area scale factor equals the linear scale factor squared: 4² = 16.
- 2Multiply the smaller area by this area scale factor.
- 312 × 16 = 192.
- 4The larger polygon's area is therefore 192 cm².
Answer: 192 cm²
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Start practisingCommon mistake. Pupils often multiply the area by the same linear scale factor used for lengths, forgetting that area scales by the square of that factor. Always square the linear scale factor before applying it to areas.
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