# Similar shapes

Shapes with the same angles but different sizes. Matching sides are in the same ratio, called the scale factor.

Maths (school) · Part 07: Shape and space · Card 6 of 9 · Last updated 2026-10-19

## Analogy

Like a photo and its enlargement: same picture, different size.

## Example

**3-4-5 and 6-8-10 triangles**

Scale factor = 6 / 3 = 2
Lengths x 2
Areas x 4
Volumes x 8

## In practice

Map makers use similar shapes to shrink a real town onto paper.

## Practice

### Flashcards

- **Lengths are doubled. What happens to the area?** It is multiplied by 4 (2 squared).

### Interview questions

**Two similar triangles have corresponding sides 3 cm and 6 cm. Explain what happens to the area and why.**

- Scale factor is 2
- Lengths are multiplied by 2
- Area scales by 2 squared
- So the area is 4 times larger

## Questions people ask

### How do you find a missing side in similar shapes?

Find the scale factor by dividing a known pair of matching sides (new over old). Then multiply the matching side by it. If 3 became 6, the factor is 2, so a side of 4 becomes 8. Always pair up sides from the same position in each shape, such as shortest with shortest.

### Why does area change by the scale factor squared?

Area has two dimensions, length and width, and both grow by the scale factor. So the area grows by the factor times itself. For a factor of 2, area grows by 2 x 2 = 4. Volume changes by the scale factor cubed, as three dimensions all grow by the same amount.

## Related concepts

- [Congruent shapes](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-5)
- [Bearings](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-7)
- [Vectors](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-8)
- [Constructions](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-9)

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