Scaling

Similar shapes and the square–cube law

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Scaling by $k$ multiplies lengths by $k$, areas by $k^2$, and volumes by $k^3$.
• Similar triangles have matching angles and proportional sides. That’s why shadows can measure heights.
• The square–cube law limits how big animals and structures can get.

Steps

1. Double it
2. Lengths, areas, volumes
3. Similar triangles
4. Shadows
5. Map area
6. Why giants can’t exist