PEAZIT Aha card
Go straight to resources ↓Double lengths do not mean double area
Similarity multiplies every length by the same positive factor k. Area has two dimensions, giving k²; volume has three, giving k³.
| Relation | Meaning |
|---|---|
| k = 6 / 3 = 2 | The factor is new length divided by original length. |
| S₂ = k²S₁ = 4S₁ | Both area dimensions double. |
| V₂ = k³V₁ = 8V₁ | For solids, all three dimensions double. |
One worked example
- k = 6 / 3 = 2The factor is new length divided by original length.
- S₂ = k²S₁ = 4S₁Both area dimensions double.
- V₂ = k³V₁ = 8V₁For solids, all three dimensions double.
Watch out: All lengths must change by the same factor. Stretching width alone is not similarity.
Goal, prerequisites and card origin
What you will learn: Convert a length scale factor into area and volume factors.
What you need first: Rectangle area and powers.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Similarity multiplies every length by the same positive factor k. Area has two dimensions, giving k²; volume has three, giving k³.