1. Scale Drawings
Lesson 3.4.4

2. Scale Drawings 3.4.4 California Standard: What it means for you:
Lesson
3.4.4
Scale Drawings
California Standard:
Measurement and Geometry 1.2
Construct and read drawings and models made to scale.
What it means for you:
You’ll learn how to draw pictures that accurately represent real places or objects. You’ll also use drawings to find information about the places or objects they represent.
Key words:
scale drawing
scale factor
measurement
distance
scale

3. Lesson
3.4.4
Scale Drawings
Scale drawings often show real objects or places — maps are good examples of scale drawings.
4 cm : 1 mile N
All the measurements on the drawing are related to the real-life measurements by the same scale factor.
So if you know the scale factor, you can figure out what the real-life measurements are.

4. Scale Drawings 3.4.4 To Make Scale Drawings You Need Real Measurements
Lesson
3.4.4
Scale Drawings
To Make Scale Drawings You Need Real Measurements
To make a scale drawing of an object or place, you need two things.
First, you need the real-life measurements of what you’re going to draw.
Second, you need a scale. This will tell you what the distances on the drawing represent. The scale is usually written as a ratio.
If 1 inch on the drawing represents 10 feet in real life, the scale is 1 inch : 10 feet.

5. Lesson
3.4.4
Scale Drawings
Example 1
A rectangular yard has a length of 24 feet and a width of 20 feet. Make a scale drawing using a scale of 1 inch : 4 feet.
Solution
You need to find the length and width of the yard in the drawing.
To convert the real-life length into a length for the drawing, set up a proportion using the scale given.
Let x be the length the yard in the drawing should be.
Drawing length
Real-life length =
1 inch
4 feet x
24 feet
Solution continues…
Solution follows…

6. Lesson
3.4.4
Scale Drawings
Example 1
A rectangular yard has a length of 24 feet and a width of 20 feet. Make a scale drawing using a scale of 1 inch : 4 feet.
Solution (continued)
Now solve the proportion to find x:
1 inch
4 feet x =
24 feet
1 inch × 24 feet
4 feet
= x ×
24 feet
= x
Multiply both sides by 24 ft
So, x = 1 inch ×
= 1 inch × 6 = 6 inches
24 feet
4 feet
Solution continues…

7. Lesson
3.4.4
Scale Drawings
Example 1
A rectangular yard has a length of 24 feet and a width of 20 feet. Make a scale drawing using a scale of 1 inch : 4 feet.
Solution (continued)
Repeat the process using y for the width of the drawing and you find:
y = 1 inch ×
= 1 inch × 5 = 5 inches
20 feet
4 feet
6 in
5 in
You can use these measurements to make a scale drawing.

8. Scale Drawings 3.4.4 Guided Practice Make the following scale drawing:
Lesson
3.4.4
Scale Drawings
Guided Practice
Make the following scale drawing:
1. A square of side length 4 m, using the scale 1 cm : 1 m.
4 cm
1 cm : 1 m, multiply both sides by 4, 4 m : 4 cm
Solution follows…

9. Scale Drawings 3.4.4 Guided Practice Make the following scale drawing:
Lesson
3.4.4
Scale Drawings
Guided Practice
Make the following scale drawing:
2. A rectangle measuring 40 in. by 60 in., using the scale 1 in. : 20 in.
2 in.
3 in.
1 in. : 20 in., multiply both sides by 2, 2 in. : 40 in. multiply both sides by 3, 3 in. : 60 in.
Solution follows…

10. Scale Drawings 3.4.4 Guided Practice
Lesson
3.4.4
Scale Drawings
Guided Practice
Make the following scale drawings:
3. A rectangular room measuring 6 ft by 12 ft, using the scale 1 in. : 3 ft.
4. A circular pond with diameter 3 m, using the scale 1 cm : 2 m.
2 in.
4 in.
1 in. : 3 ft, multiply both sides by 2, 2 in. : 6 ft multiply both sides by 4, 4 in. : 12 ft
1 cm : 2 m, multiply both sides by 1.5, 1.5 cm : 3 m
diameter= 1.5 cm
Solution follows…

11. Scale Drawings 3.4.4 You Can Use Scale Drawings to Find Actual Lengths
Lesson
3.4.4
Scale Drawings
You Can Use Scale Drawings to Find Actual Lengths
The size of real objects can be found by measuring scale drawings.

12. Lesson
3.4.4
Scale Drawings
Example 2
This map shows three towns. Find the real-life distances between:
Town A
Town B
Town A and Town B
Town A and Town C
Town C
Solution
Scale — 1 grid square : 2.5 miles
The distance between Town A and Town B on the map is 6 grid squares.
The scale tells us that 1 grid square represents 2.5 miles, so the distance between Town A and Town B is: 6 × 2.5 miles = 15 miles.
Solution continues…
Solution follows…

13. Lesson
3.4.4
Scale Drawings
Example 2
This map shows three towns. Find the real-life distances between:
Town A
Town B
Town A and Town B
Town A and Town C
Town C
Solution (continued)
Scale — 1 grid square : 2.5 miles
Town A and Town C are 3 grid squares apart on the map.
In real life this is equal to 3 × 2.5 miles = 7.5 miles.

14. Scale Drawings 3.4.4 Guided Practice
Lesson
3.4.4
Scale Drawings
Guided Practice
This picture shows a scale drawing of the living room in Lashona’s house. The scale used is 2 in. : 3 feet.
In Exercises 5–8, find the real-life measurements of:
5. The chair
6. The couch
7. The bookcase
8. The rug
1 in.
Bookcase
3.4 in.
2 in.
1.5 in.
3 ft × 3 ft
TV set
Couch
4 in.
Rug
3.2 in.
3 ft × 6 ft
2 in.
1.5 ft × 5.1 ft
Chair
2 in.
2.25 ft × 4.8 ft
Solution follows…

15. Lesson
3.4.4
Scale Drawings
You Can Sometimes Find Real Lengths Without a Scale
If you know one of the real-life lengths shown on a scale drawing, then you can figure out the others without a scale.

16. Lesson
3.4.4
Scale Drawings
Example 3
This scale drawing shows three classrooms at Gabriel’s school.
Gabriel measures the drawing. His measurements are shown in red.
Gabriel knows Room 207 is 4.2 m wide in real life. What is the real-life width of Room 208?
3 cm
3.5 cm
Room 208
Room 209
Room 207
Solution
You can find the answer by setting up a proportion, similar to the one in Example 1.
Use x for the real-life width of Room 208.
Solution continues…
Solution follows…

17. Lesson
3.4.4
Scale Drawings
Example 3
This scale drawing shows three classrooms at Gabriel’s school.
Gabriel measures the drawing. His measurements are shown in red.
Gabriel knows Room 207 is 4.2 m wide in real life. What is the real-life width of Room 208?
3 cm
3.5 cm
Room 208
Room 209
Room 207
Solution (continued)
Real-life width
Drawing width =
4.2 m
3 cm x
3.5 cm
x = 4.2 m ×
= 4.9 m
3.5 cm
3 cm
So the width of Room 208 is 4.9 m in real life.

18. Scale Drawings 3.4.4 Guided Practice
Lesson
3.4.4
Scale Drawings
Guided Practice
Use the map below to answer Exercises 9–13. It is 18 miles from Town D to Town E. Calculate the distance from:
9. Town D to Town F
10. Town F to Town G
11. Town G to Town J
12. Town H to Town J
13. Town D to Town G
Town D
Town E
18 miles
24 miles
Town F
Town G
12 miles
Town H
Town J
30 miles
30 miles
Solution follows…

19. Scale Drawings 3.4.4 Guided Practice
Lesson
3.4.4
Scale Drawings
Guided Practice
Use the map below to answer Exercise 14. It is 18 miles from Town D to Town E.
Town D
Town E
14. Find the number that completes the following sentence: The scale on this map is 1 grid square : ____ miles.
Town F
Town G 6
Town H
Town J
Solution follows…

20. Scale Drawings 3.4.4 Independent Practice
Lesson
3.4.4
Scale Drawings
Independent Practice
1. A sail for a boat is in the shape of a right triangle. The actual height of the sail is 18 feet, and it has a base of 12 feet. Make a scale drawing of the sail using a scale of 1 cm : 3 ft.
4 cm
6 cm
Solution follows…

21. Scale Drawings 3.4.4 Independent Practice
Lesson
3.4.4
Scale Drawings
Independent Practice
2. This sketch of a house has not been drawn to scale.
Make a scale drawing of the house using a scale of 1 cm : 6 ft.
36 feet
18 feet
6 feet
6 cm
3 cm
1 cm
Solution follows…

22. Scale Drawings 3.4.4 Independent Practice
Lesson
3.4.4
Scale Drawings
Independent Practice
3. A scale model of a town uses a scale of 1 inch : 30 feet. Find the actual height of a building that is 2.5 in. tall in the model.
4. On a map, 2 inches represents 45 miles. What does one inch represent on this map?
75 feet
22.5 miles
Solution follows…

23. Scale Drawings 3.4.4 Independent Practice
Lesson
3.4.4
Scale Drawings
Independent Practice
Amanda is drawing a plan of her bedroom using a scale of 1 in : 2 ft. Exercises 5–7 show objects from the plan. Calculate the real-life dimensions of the objects.
1.5 in.
3 in.
1.75 in.
1 in.
3.5 ft × 2 ft
3 ft × 6 ft
Desk
3.5 in.
1.5 in.
7 ft × 3 ft
Bed
Chest of drawers
Solution follows…

24. Scale Drawings 3.4.4 Independent Practice
Lesson
3.4.4
Scale Drawings
Independent Practice
The scale drawing below shows part of a zoo. The parrot enclosure measures 40 m by 24 m. Find the following real-life measurements:
8. The length and width of the sea lion enclosure.
9. The length and width of the lemur enclosure.
Parrots
Cobras
32 m × 48 m
Lemurs
32 m × 88 m
Sea Lions
Turtles
Solution follows…

25. Scale Drawings 3.4.4 Independent Practice
Lesson
3.4.4
Scale Drawings
Independent Practice
The scale drawing below shows part of a zoo. The parrot enclosure measures 40 m by 24 m. Find the following real-life measurements:
10. The perimeter of the turtle enclosure.
11. The area of the cobra enclosure.
Parrots
Cobras
144 m
Lemurs
Sea Lions
1280 m2
Turtles
Solution follows…

26. Scale Drawings 3.4.4 Round Up
Lesson
3.4.4
Scale Drawings
Round Up
Pictures that are drawn to scale can be very useful.
If maps weren’t made to scale, they would be much harder to use. And if plans and blueprints for buildings or machines weren’t done as scale drawings, it would be difficult to build them the right size and shape.