# 4.8: Read and Interpret Scale Drawings and Floor Plans

**At Grade**Created by: CK-12

**Practice**Distances or Dimensions Given Scale Measurements

Have you ever helped build or design a playground? Take a look at this dilemma.

The local community is planning to put a playground in the space provided. This is the drawing that they have created. You can see that the width of the playground is 7 inches wide in the drawing. If this is the case, what is the actual width of the playground?

Use what you learn in this Concept to help you solve this dilemma.

### Guidance

**A** *scale drawing***or floor plan is a representation of an actual object or space drawn in two-dimensions.** For a floor plan, you can imagine that you are directly above the building looking down. The lines represent the walls of the building, and the space in between the lines represents the floor.

**In order to find the actual dimensions from a floor plan, you can set up and solve a proportion. The scale given in the drawing is the first ratio. The unknown length and the scale length is the second ratio.**

**This floor plan shows several classrooms at Craig’s school. The length of Classroom 2 in the floor plan is 2 inches. What is the actual length, in feet, of Classroom 2?**

**Set up a proportion.** The scale in the drawing says that \begin{align*}\frac{1}{2} \ inch = 3 \ feet\end{align*}. So set up a ratio using these values: \begin{align*}\frac{0.5 \ inch}{3 \ feet}\end{align*}.

**Now write the second ratio.** You know the scale length is 2 inches. The unknown length is \begin{align*}x\end{align*}. Make sure that the second ratio follows the form of the first ratio: inches over feet.

\begin{align*}\frac{0.5 \ inch}{3 \ feet} = \frac{2 \ inches}{x \ feet}\end{align*}

Now cross-multiply to solve for \begin{align*}x\end{align*}.

\begin{align*}(0.5)x &= 2(3)\\ 0.5x &= 6\\ x &= 12\end{align*}

**The actual length of the classroom is 12 feet.**

If the scale said 1/2" = 4 feet, what would be the inches drawn for each room?

#### Example A

\begin{align*}8\end{align*}' x \begin{align*}12\end{align*}'

**Solution: \begin{align*}1\end{align*}" x \begin{align*}1.5\end{align*}"**

#### Example B

\begin{align*}20\end{align*}' x \begin{align*}28\end{align*}'

**Solution: \begin{align*}2.5\end{align*}" x \begin{align*}3.5\end{align*}"**

#### Example C

\begin{align*}16\end{align*}' x \begin{align*}24\end{align*}'

**Solution: \begin{align*}2\end{align*}" x \begin{align*}3\end{align*}"**

Now let's go back to the dilemma from the beginning of the Concept.

**To work on this problem, first, let’s write a ratio to show the scale.**

\begin{align*}\frac{1^{\prime\prime}}{20 \ ft}\end{align*}

**Next, we can write a proportion showing the scale to the inches on the drawing.**

\begin{align*}\frac{1^{\prime\prime}}{20 \ ft} &= \frac{7^{\prime\prime}}{x}\\ x &= 140 \ feet\end{align*}

**The width of the playground is 140 feet.**

**Notice that whether you are working with floor plans, scale drawings or maps, you are still working to create a proportion and solve for the missing measurements.**

### Vocabulary

- Ratio
- a way of comparing two quantities using a colon, fraction form or by using the word “to.”

- Proportion
- showing two equal ratios. Two equal ratios form a proportion.

- Similar Figures
- figures that are the same shape but different sizes.

- Scale Drawing
- a drawing that is done with a scale so that specific small units of measure represent larger units of measure.

### Guided Practice

Here is one for you to try on your own.

This scale drawing shows the fountain in front of a hotel. The diameter of the fountain in the scale drawing is 4 centimeters. What is the actual diameter of the fountain?

**Solution**

Set up a proportion. Write the scale as a ratio.

\begin{align*}\frac{1 \ cm}{0.5 \ m}\end{align*}

Now write the second ratio, making sure it follows the form of the first ratio.

\begin{align*}\frac{1 \ cm}{0.5 \ m} = \frac{4 \ cm}{x \ m}\end{align*}

Now cross-multiply and solve for \begin{align*}x\end{align*}.

\begin{align*}(1)x &= 4(0.5)\\ x &= 2\end{align*}

**The actual diameter of the fountain is 2 meters.**

### Video Review

### Practice

Directions: This floor plan shows Bonnie’s house. Use it to answer the following questions.

- The width of the bedroom on the floor plan measures 1.5 inches. What is the actual width of the bedroom?
- The length of the kitchen on the floor plan measures 3 inches. What is the actual length of the kitchen?
- The study measures 2 inches by 1.5 inches on the floor plan. What is the actual area of the study?
- The study measures 2 inches by 1.5 inches on the floor plan. What is the actual perimeter of the study?
- The study measures 2 inches by 1.5 inches on the floor plan. What are the actual dimensions of the study?
- If the length of the bedroom is the same as the study, what are the actual dimensions of the bedroom?
- What is the area of the bedroom?
- What is the actual length of the outside of the house?

Directions: Answer each question.

- A square measures 10 inches on each side. What is it's area?
- If the scale is 1" = 50 ft, what is the actual side length of the same square?
- What is it's area?
- A classroom measures 21 feet by 15 feet. A second classroom has a similar size but the dimensions are \begin{align*}\frac{1}{3}\end{align*} as long. How does the area of the second classroom compare to the area of the first classroom?
- What are the dimensions of the second classroom?
- Yuri’s backyard has an area of 1,000 square feet. The dimensions of Kyle’s backyard are all \begin{align*}\frac{1}{5}\end{align*} the size of Yuri’s. What is the area of Kyle’s backyard?
- Mary's yard is double the area of Kyle's backyard. What is the area of Mary's yard?

Inches

An inch is a customary unit of measurement, measured best by a ruler.Length

Length is a measurement of how long something is. Examples of customary units of length are inches, feet, yards and miles.Proportion

A proportion is an equation that shows two equivalent ratios.Scale Drawing

A scale drawing is a drawing that is done with a scale so that specific small units of measure represent larger units of measure.Similar

Two figures are similar if they have the same shape, but not necessarily the same size.Two – Dimensional

A figure drawn in two dimensions is only drawn using length and width.### Image Attributions

Here you'll learn to interpret scale drawings and floor plans.

Inches

An inch is a customary unit of measurement, measured best by a ruler.Length

Length is a measurement of how long something is. Examples of customary units of length are inches, feet, yards and miles.Proportion

A proportion is an equation that shows two equivalent ratios.Scale Drawing

A scale drawing is a drawing that is done with a scale so that specific small units of measure represent larger units of measure.Similar

Two figures are similar if they have the same shape, but not necessarily the same size.Two – Dimensional

A figure drawn in two dimensions is only drawn using length and width.