Scale Drawings Examples: 25 Problems with Answers

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 multiplies every real length by the same scale factor, keeping shape while changing size.

Common stuck point: The procedure for scale drawings is the easy part; the trap is multiplying area by the linear scale factor. Asking "Is every length related to the real object by one fixed multiplier (the scale factor)?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Is every length related to the real object by one fixed multiplier (the scale factor)?

Worked Examples

Example 1

easy

A map has a scale of

1

: 50

km. Two cities are

3.5

cm apart on the map. What is the actual distance between the cities?

Map segment: 3.5 cm represents the actual distance to find (175 km)

Answer

175

First step

Step 1: Identify the scale factor:

1

cm on the map

= 50

km in reality.

Full solution

2
Step 2: Write the proportion: $\frac{1 \text{ cm}}{50 \text{ km}} = \frac{3.5 \text{ cm}}{x \text{ km}}$ .
3
Step 3: Solve by cross-multiplying: $x = 3.5 \times 50 = 175$ km.
4
Step 4: The actual distance between the two cities is $175$ 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?

Floor plan drawing (1/4 in = 1 ft): find the actual dimensions and area

Example 3

medium

An architect's drawing has scale

\tfrac{1}{2}\text{ inch} = 1\text{ foot}

. A wall is drawn

7

inches long. How long is the real wall?

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?

Model car at 1:24 scale — find the real length (answer: 3.6 m)

Example 2

hard

A park is drawn on a map using a scale of

2

: 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).

Park on map (2 cm : 300 m) — find actual area (337,500 m²

Example 3

easy

A map uses scale

1\text{ cm} : 20\text{ km}

. A river is

7

cm long on the map. How long is it in reality?

Example 4

easy

A model bridge at scale

1:80

25

cm long. How long is the real bridge in meters?

Example 5

easy

A real garden is

40

m wide. On a scale

1:500

map, how wide is it?

Example 6

easy

A map scale is

1:50{,}000

. Two landmarks are

4

cm apart. How far apart are they in km?

Example 7

easy

Scaling lengths by factor

k = 3

multiplies the area by what factor?

Example 8

medium

A floor plan at scale

1:40

shows a room

5

\times

8

cm. Find the room's real area in

\text{m}^2

Example 9

medium

A scale model of a building is at

1:75

. The model is

40

cm tall. How tall is the real building in meters?

Example 10

medium

A rectangular park is

300

m by

500

m. Drawn on a map at scale

1:10{,}000

, what are the map dimensions in cm?

Example 11

medium

A scale drawing has scale

1:25

. The real area of a plot is

625

^2

. What is the drawing's area in cm

^2

Example 12

medium

Two maps cover the same region: scale

1:25{,}000

and

1:100{,}000

. A road is

8

cm long on the more detailed map. How long is it on the less detailed map?

Example 13

medium

A toy train is at scale

1:87

. The real locomotive is

20

m long. How long is the model in cm?

Example 14

medium

1:20

model boat holds

0.5

L of water. How much does the real boat hold (assuming volume scaling)?

Example 15

hard

A lake covers

3.2

^2

in reality and

20

^2

on a map. Find the linear scale

1:n

Example 16

hard

Two similar triangles have areas

32

and

50

. Find the ratio of their corresponding sides.

Example 17

hard

Two similar prisms have volumes

54

^3

and

128

^3

. Find the ratio of their surface areas.

Example 18

hard

A blueprint shows a rectangle

4

\times

3

cm at scale

1:50

. The real rectangle's diagonal is how long?

Example 19

hard

1:30

model truck has a fuel tank that holds

50

mL of liquid. Estimate how many liters the real truck's tank holds.

Example 20

hard

A scale model of a sculpture (scale

1:6

) weighs

4

kg and is made of the same material as the original. Find the original's mass.

Example 21

challenge

An architect draws a

30

m tall tower on A4 paper that is

29.7

cm tall, allowing

3

cm of margin at the top and bottom. What is the largest sensible scale

1:n

(smallest

n

) usable, with

n

a round multiple of

50

Example 22

challenge

1:25

model of a swimming pool holds

32

L of water. The real pool's owner wants to know how many cubic meters fill it.

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Related Concepts

Ratios Proportions Multiplication Similarity Dilation Similarity Criteria

Background Knowledge

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

ratiosproportionsmultiplicationsimilarity