Scale Drawings & Scale Drawings & ModelsModels

Section 4.6Section 4.6

Section 4.6: Scale Drawings & ModelsSection 4.6: Scale Drawings & Models

Distances on a scale drawing Distances on a scale drawing or model are proportional to or model are proportional to real-life distances. The real-life distances. The scalescale is determined by the ratio of a is determined by the ratio of a length on a drawing or model length on a drawing or model to its corresponding actual to its corresponding actual length.length.

ExamplesExamples

The local school district has made a scale The local school district has made a scale model of a campus of Engels Middle model of a campus of Engels Middle School including a proposed new building. School including a proposed new building. The scale of the model is 1 inch = 3 feet.The scale of the model is 1 inch = 3 feet.

Gym

Academic Building

Parking

New Building

Example Continued…Example Continued…

An existing gym is 8 inches tall in the An existing gym is 8 inches tall in the model. How tall is the actual gymnasium?model. How tall is the actual gymnasium?

Gym

Academic Building

Parking

New Building 1 8

3 X=

Set up a proportion…

1(x) = 3(8)

X = 24 feet tall

Section 4.6Section 4.6To find the scale factor for scale drawings To find the scale factor for scale drawings

and models, write the ratio given by the and models, write the ratio given by the scale in scale in simplest form.simplest form.

Write the ratio of 1 inch to 1 feet in Write the ratio of 1 inch to 1 feet in simplest form.simplest form.

1 inch1 inch 1 in.1 in.

11 Feet Feet 16 in.16 in.

1

3

1

3

=Conversion:1 foot = 12

inches

Example…Example…

On a map, two cities are 5On a map, two cities are 5 inches apart. inches apart. The scale of the map is 0.5 inch = 3 miles. The scale of the map is 0.5 inch = 3 miles. What is the actual distance between the towns?What is the actual distance between the towns?

34

Set up a proportion.

0.5 inch 5 inch

3 miles X miles

34

=

0.5X = 3(5 )

0.5X = 17.25

X = 34.5 miles

34

ExampleExampleMarta is making a scale drawing of her Marta is making a scale drawing of her

apartment for a school project. The apartment apartment for a school project. The apartment is 28 feet wide. On her drawing, the apartment is 28 feet wide. On her drawing, the apartment is 7 inches wide. What is the scale of Marta’s is 7 inches wide. What is the scale of Marta’s drawing?drawing?

Set up a proportion. 28

feet28 feet 4 feet

7 inches 1 inch=

1 inch = 4 feet