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Scale Drawings Lesson 3.4.4

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**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

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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.

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**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.

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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…

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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…

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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.

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**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…

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**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…

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**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…

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**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.

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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…

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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.

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**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…

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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.

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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…

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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.

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**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…

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**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…

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**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…

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**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…

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**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…

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**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…

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**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…

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**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…

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**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.

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