This document contains information about using scale drawings and scale factors to solve geometry problems involving real-world objects and distances. It includes examples of using scale drawings of maps to find actual distances between locations by setting up proportions from the scale. It also demonstrates how to find the actual size of an object drawn on a scale drawing or model by again using proportions and scale factors. The document emphasizes that geometry helps describe real-world objects by allowing accurate representations using scale drawings and conversions between actual sizes and scaled sizes.

1. Course 2, Lesson 7-4
Use the make a model strategy to solve Exercises 1 and 2.
A 15-inch by 20-inch piece of poster board has a 3.5-inch square cut
out of each corner. Then the sides are folded up and taped together to
make an open box.
1. Find the surface area of the box.
2. Find the volume of the box.
3. Edward is rearranging the 132 square tables in the cafeteria to make
long tables. If he uses five tables to make one long table, how many
long tables can he make?
4. How many tables will be left over?

2. Course 2, Lesson 7-4
ANSWERS
1. 251 in²
2. 364 in³
3. 26 long tables
4. 2 tables

3. Geometry
Course 2, Lesson 7-4
HOW does geometry help us
describe real-world objects?

4. Course 2, Lesson 7-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Geometry
• 7.G.1
Solve problems involving scale drawings of geometric figures,
including computing actual lengths and areas from a scale drawing
and reproducing a scale drawing at a different scale.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.

5. • To use a scale drawing or a
scale model
• To find a scale factor
Course 2, Lesson 7-4
Geometry

6. Course 2, Lesson 7-4
Geometry
• scale drawing
• scale model
• scale
• scale factor

7. 1
Need Another Example?
2
3
Step-by-Step Example
1. What is the actual distance
between Hagerstown and
Annapolis?
Use a centimeter ruler to find the map distance between the
two cities. The map distance is about 4 centimeters.
Write and solve a proportion using the scale. Let d
represent the actual distance between the cities.
1 × d = 24 × 4 Cross products
The distance between the cities is about 96 miles.
d = 96 Simplify.

8. Answer
Need Another Example?
Refer to the map of Florida below. What is the actual
distance between Daytona Beach and Orlando? Use
a ruler to measure. The map distance is about 1.5
inches.
about 51 mi

9. 1
Need Another Example?
2
3
Step-by-Step Example
2. A graphic artist is creating
an advertisement for this
cell phone. If she uses a
scale of 5 inches = 1 inch,
what is the length of the
cell phone on the
advertisement?
Write a proportion using the scale. Let a represent the
length of the advertisement cell phone.
5 • 4 = 1 • a Cross products
The length of the cell phone on the advertisement is
20 inches long.
20 = a Simplify.

10. Answer
Need Another Example?
An artist is painting a large mural of flowers on the
side of a school. If she uses the scale 4 inches = 1 inch,
how large will the mural painting of a rose bloom be if the
actual height of the rose bloom is 6 inches?
25 in.

11. 1
Need Another Example?
2
Step-by-Step Example
3. Find the scale factor of a model sailboat if the scale
is 1 inch = 6 feet.
The scale factor is .
Convert 6 feet to inches.
Divide out the common units.

12. Answer
Need Another Example?
Find the scale factor of a blueprint if the scale is
1 inch = 3 feet.

13. 1
Need Another Example?
2
3
Step-by-Step Example
4. A floor plan for a home is
shown at the left where inch
represents 3 feet of the actual
home. What is the actual area
of bedroom 1?
So, the area of bedroom 1 is 24 × 6 or 144 square feet.
Find cross products.w = 12
w = 24
Find cross products.
Divide each side by .
x = 3
x = 6
Length of Bedroom 1. Width of Bedroom 1.
Divide each side by .

14. Answer
Need Another Example?
Refer to the diagram at the
right. What is the actual area
of the hallway?
108 ft2

15. How did what you learned
today help you answer the
Course 2, Lesson 7-4
Geometry
HOW does geometry help us
describe real-world objects?

16. How did what you learned
today help you answer the
Course 2, Lesson 7-4
Geometry
HOW does geometry help us
describe real-world objects?
Sample answers:
• By using scale drawings and scale models to represent
objects too large or too small to be drawn or built at
actual size
• By finding the actual distance between two points on a
map

17. A map has a scale of
1 inch = 125 miles. Write about
how you could find the actual
distance between two points
shown on the map.
Course 2, Lesson 7-4
Ratios and Proportional RelationshipsFunctionsGeometry