Scale drawings
Scale Drawings
Scale Drawings is a topic in Similarity in the Texas Essential Knowledge and Skills (Geometry, §111.41). It is aligned to Standard G.7(B), which requires students to apply the proportionality of similar figures to solve problems involving 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.