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1 Lesson Scale Drawings

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2 Lesson 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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3 Scale Drawings Lesson Scale drawings often show real objects or places — maps are good examples of scale drawings. So if you know the scale factor, you can figure out what the real-life measurements are. All the measurements on the drawing are related to the real-life measurements by the same scale factor. 4 cm : 1 mile N

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4 Scale Drawings To Make Scale Drawings You Need Real Measurements Lesson If 1 inch on the drawing represents 10 feet in real life, the scale is 1 inch : 10 feet. 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.

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5 Scale Drawings Example 1 Solution follows… Lesson 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. Solution continues… Let x be the length the yard in the drawing should be. Drawing length Real-life length = 1 inch 4 feet x = 24 feet

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6 1 inch × 24 feet 4 feet = x × 24 feet = x Now solve the proportion to find x : Scale Drawings Example 1 Lesson 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) Multiply both sides by 24 ft So, x = 1 inch ×= 1 inch × 6 = 6 inches 24 feet 4 feet 1 inch 4 feet x = 24 feet Solution continues…

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7 Repeat the process using y for the width of the drawing and you find: Scale Drawings Example 1 Lesson 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) You can use these measurements to make a scale drawing. y = 1 inch ×= 1 inch × 5 = 5 inches 20 feet 4 feet 6 in 5 in

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8 Scale Drawings Guided Practice Solution follows… Lesson 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

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9 Scale Drawings Guided Practice Solution follows… Lesson 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.

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10 Scale Drawings Guided Practice Solution follows… Lesson 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. diameter = 1.5 cm 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

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11 Scale Drawings You Can Use Scale Drawings to Find Actual Lengths Lesson The size of real objects can be found by measuring scale drawings.

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12 Scale Drawings Example 2 Solution follows… Lesson Town A and Town B Town A and Town C This map shows three towns. Find the real-life distances between: Town A Town B Town C Scale — 1 grid square : 2.5 miles Solution 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…

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13 Town A and Town C are 3 grid squares apart on the map. Scale Drawings Example 2 Lesson Town A and Town B Town A and Town C This map shows three towns. Find the real-life distances between: Town A Town B Town C Scale — 1 grid square : 2.5 miles Solution (continued) In real life this is equal to 3 × 2.5 miles = 7.5 miles.

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14 Scale Drawings Guided Practice Solution follows… Lesson 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 Bookcase Couch Chair TV set Rug 1 in. 3.4 in. 1.5 in. 3.2 in. 2 in. 4 in. 2 in. 3 ft × 3 ft 3 ft × 6 ft 1.5 ft × 5.1 ft 2.25 ft × 4.8 ft

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15 Scale Drawings You Can Sometimes Find Real Lengths Without a Scale Lesson 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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16 Scale Drawings Example 3 Solution follows… Lesson 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? Room 207 Room 208 Room cm 3.5 cm 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…

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17 Scale Drawings Example 3 Lesson 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? Room 207 Room 208 Room cm 3.5 cm Solution (continued) So the width of Room 208 is 4.9 m in real life. 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

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18 Scale Drawings Guided Practice Solution follows… Lesson 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 DTown E Town FTown G Town HTown J 18 miles 24 miles 12 miles 30 miles

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19 Scale Drawings Guided Practice Solution follows… Lesson Use the map below to answer Exercise 14. It is 18 miles from Town D to Town E. Town DTown E Town FTown G Town HTown J 14. Find the number that completes the following sentence: The scale on this map is 1 grid square : ____ miles. 6

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20 Scale Drawings Independent Practice Solution follows… Lesson 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

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21 Scale Drawings Independent Practice Solution follows… Lesson 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. 6 cm 3 cm 1 cm 36 feet 18 feet 6 feet

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22 Scale Drawings Independent Practice Solution follows… Lesson 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

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23 Scale Drawings Independent Practice Solution follows… Lesson 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 in. 3 in in. 1 in. 3.5 in. 1.5 in. 3 ft × 6 ft 3.5 ft × 2 ft 7 ft × 3 ft Bed Chest of drawers Desk

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24 Scale Drawings Independent Practice Solution follows… Lesson The scale drawing below shows part of a zoo. The parrot enclosure measures 40 m by 24 m. Find the following real-life measurements: 32 m × 48 m 32 m × 88 m 8. The length and width of the sea lion enclosure. 9. The length and width of the lemur enclosure. Sea Lions Parrots Cobras Turtles Lemurs

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25 Scale Drawings Independent Practice Solution follows… Lesson 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. 144 m 1280 m 2 Sea Lions Parrots Cobras Turtles Lemurs

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26 Scale Drawings Round Up Lesson 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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