Mathematics · Grades 7–10
Scale factors and area
A length scale factor k changes area by k squared.
The key idea
A length scale factor k changes area by k squared.
new area = old area × k²
Worked examples
A shape has area 64 cm². All lengths are multiplied by 2. Find the new area in cm².
64 × 2² = 256
256 cm²
A shape has area 46 cm². All lengths are multiplied by 5. Find the new area in cm².
46 × 5² = 1150
1150 cm²
Try it yourself
A shape has area 50 cm². All lengths are multiplied by 5. Find the new area in cm².
A shape has area 7 cm². All lengths are multiplied by 9. Find the new area in cm².
Check your understanding
Answers and marking notes
- 1250 cm²
50 × 5² = 1250
- 567 cm²
7 × 9² = 567
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.