Scale Drawings

What Is a Scale Drawing?

A scale drawing is a proportional representation of an object (larger or smaller).

The scale tells the ratio of the drawing size to actual size.

Scale Factor

$\text{Scale factor} = \frac{\text{Drawing measurement}}{\text{Actual measurement}}$

Example: Scale of $1 \text{ in} : 50 \text{ ft}$

If a room is 3 inches on the drawing: $\text{Actual length} = 3 \times 50 = 150 \text{ ft}$

Finding Actual Dimensions

If scale is $1 : 200$ and drawing length is 4 cm: $\text{Actual} = 4 \times 200 = 800 \text{ cm} = 8 \text{ m}$

Finding Drawing Dimensions

If scale is $1 \text{ cm} : 5 \text{ m}$ and actual length is 30 m: $\text{Drawing} = 30 \div 5 = 6 \text{ cm}$

Scale Factor and Area

If the scale factor for length is $k$, then:

• Lengths scale by $k$
• Areas scale by $k^2$

If a room is 3× bigger in each dimension, its area is $3^2 = 9$ times bigger!

Maps

Maps use scales like $1 \text{ in} = 10 \text{ miles}$.

If two cities are 4.5 inches apart on the map: $4.5 \times 10 = 45 \text{ miles apart}$

Practice: Measure your room and create a scale drawing using a scale of 1 cm = 1 foot.