Addressing Standard 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.

Objective

When I know the actual measurements, I can create a scale drawing at a given scale.

I know how different scales affect the lengths in the scale drawing.

I can determine the scale of a scale drawing when I know lengths on the drawing and corresponding actual lengths.

Online Workbook

Take me to the website.

Llévame al sitio web.

Lesson Summary

If we want to create a scale drawing of a room's floor plan that has the scale “1 inch to 4 feet,” we can divide the actual lengths in the room (in feet) by 4 to find the corresponding lengths (in inches) for our drawing.

A scale drawing of a room's floor plan. A scale is shown indicating 1 inch equals 4 feet.

Suppose the longest wall is 15 feet long. We should draw a line 3.75 inches long to represent this wall, because 15÷4=3.75.

There is more than one way to express this scale.

These three scales are all equivalent, since they represent the same relationship between lengths on a drawing and actual lengths:

1 inch to 4 feet
$\frac{1}{2}$ inch to 2 feet
$\frac{1}{4}$ inch to 1 foot

Any of these scales can be used to find actual lengths and scaled lengths (lengths on a drawing). For instance, we can tell that, at this scale, an 8-foot long wall should be 2 inches long on the drawing because $\frac{1}{4} \cdot 8 = 2$ .

The size of a scale drawing is influenced by the choice of scale. For example, here is another scale drawing of the same room using the scale 1 inch to 8 feet.

A scale drawing of a room's floor plan. A scale is shown indicating 1 inch equals 8 feet.

Notice this drawing is smaller than the previous one. Since one inch on this drawing represents twice as much actual distance, each side length only needs to be half as long as it was in the first scale drawing.

Additional Practice on Khan Academy

Use this Khan Academy Link to get additional practice and supports for this lesson.