Scale drawings
Scale Drawings
Scale Drawings is a topic in Similarity in the California Common Core State Standards. It is aligned to Standard G-SRT.5, which requires students to use congruence and similarity criteria to solve problems, including with scale drawings.
A scale drawing represents an object with every length multiplied by a common scale factor, preserving all angles.
Theory
A scale drawing (map, blueprint, or model) is a similar copy of a real object. The scale is the ratio drawing : actual, such as \(1{:}50\).
- Actual length \(=\) drawing length \(\times\) scale.
- Drawing length \(=\) actual length \(\div\) scale.
- Area scales by the square of the linear scale.
The scale relationships:
How to use a scale
- Read the scale as drawing : actual.
- Multiply a drawing length by the scale for the actual length (or divide for the reverse).
- Convert units as needed.
- For area, use the scale squared.
Multiply the drawing length by the scale.
| \(8\ \text{cm}\times 50\) | \(=\) | \(400\ \text{cm}=4\ \text{m}\) |
Divide the actual length by the scale (convert to cm).
| \(\dfrac{200\ \text{cm}}{50}\) | \(=\) | \(4\ \text{cm}\) |
Multiply, then convert cm to km.
| \(6\times 100{,}000\) | \(=\) | \(600{,}000\ \text{cm}\) |
| \(=\) | \(6\ \text{km}\) |
Area scales by the square of the linear scale.
| \(50^2\) | \(=\) | \(2500\) |
So the actual floor area is \(2500\) times the plan area.
Common pitfalls
Frequently asked questions
What is a scale drawing?
A proportional (similar) representation of a real object, such as a map or blueprint, using a stated scale.
How do you find an actual length from a scale drawing?
Multiply the drawing length by the scale (with consistent units).
How does area change with the scale?
Area scales by the square of the linear scale: a \(1{:}50\) scale gives an area factor of \(50^2=2500\).
What does a scale of 1:100,000 mean?
Each unit on the map represents 100,000 of the same unit in reality.