Scale Drawings Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Scale Drawings.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Creating or interpreting drawings and models where every length is multiplied by the same constant (the scale factor), preserving shape while changing size.

A map is a scale drawing of the real world. If 1 inch on the map equals 10 miles in reality, the scale factor is 1:10\text{ miles}. Every distance on the map uses the same ratio, so the shapes stay accurate—just smaller. Enlarging a photo works the same way in reverse.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A scale drawing preserves all angles and multiplies all lengths by the same factor. Areas scale by the factor squared: if lengths double, area quadruples.

Common stuck point: Area does not scale the same way as length. If a scale factor is 1:3, areas scale by 1:9 (factor squared), not 1:3.

Worked Examples

Example 1

easy
A map has a scale of 1 cm : 50 km. Two cities are 3.5 cm apart on the map. What is the actual distance between the cities?

Solution

  1. 1
    Step 1: Identify the scale factor: 1 cm on the map = 50 km in reality.
  2. 2
    Step 2: Write the proportion: \frac{1 \text{ cm}}{50 \text{ km}} = \frac{3.5 \text{ cm}}{x \text{ km}}.
  3. 3
    Step 3: Solve by cross-multiplying: x = 3.5 \times 50 = 175 km.
  4. 4
    Step 4: The actual distance between the two cities is 175 km.

Answer

175 km
Scale drawings use proportional reasoning. The scale ratio 1:50 means every 1 cm on the map represents 50 km in reality. Multiplying the map distance (3.5 cm) by the scale factor (50) gives the actual distance of 175 km.

Example 2

medium
An architect draws a floor plan with a scale of \frac{1}{4} inch = 1 foot. A room measures 3.5 inches by 2 inches on the drawing. What are the actual dimensions and area of the room?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A model car is built at a scale of 1:24. The model car is 15 cm long. How long is the actual car in meters?

Example 2

hard
A park is drawn on a map using a scale of 2 cm : 300 m. On the map, the park is a rectangle 5 cm by 3 cm. Find the actual area of the park in square meters and in hectares (1 hectare = 10,000 m²).
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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