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Scale Measurement: Maps & Scale Drawings

Learn how to find actual distances from scale maps using simple calculations and cross products. Practice multi-step problems with scale models and conversions.

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Scale Measurement: Maps & Scale Drawings

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  1. Maps The scale of the map at the right is 1 inch : 26 miles. Find the actual distance from Pocahontas to Algona. EXAMPLE 4 Use a scale drawing SOLUTION Use a ruler. The distance from Pocahontas to Algona on the map is about 1.25 inches. Let xbe the actual distance in miles.

  2. distance on map = actual distance x 1.25 (26) = 32.5 x = 1.25 in. 1 in. xmi 26 mi EXAMPLE 4 Use a scale drawing Cross Products Property Simplify. The actual distance from Pocahontas to Algona is about 32.5 miles.

  3. Scale Model You buy a 3-D scale model of the Reunion Tower in Dallas, TX. The actual building is 560feet tall. Your model is 10 inches tall, and the diameter of the dome on your scale model is about 2.1inches. a. What is the diameter of the actual dome? About how many times as tall as your model is the actual building? b. EXAMPLE 5 Solve a multi-step problem

  4. 10 in. 2.1 in. a. measurement on model = 560ft xft measurement on actual building 10 x 1176 = x 117.6 = ANSWER The diameter of the actual dome is about 118 feet. EXAMPLE 5 Solve a multi-step problem SOLUTION Cross Products Property Solve for x.

  5. 12 in. b. To simplify a ratio with unlike units, multiply by a conversion factor. 1 ft 672 = = ANSWER The actual building is 672 times as tall as the model. 560ft 560ft 10 in. 10 in. EXAMPLE 5 Solve a multi-step problem

  6. distance on map actual distance = 4 in 1 96 mi = 24 for Examples 4 and 5 GUIDED PRACTICE 4.Two cities are 96 miles from each other. The cities are 4 inches apart on a map. Find the scale of the map. SOLUTION The distance between two cities are 96 miles, and the distance on the map is 4 inches Simplify. = 1 : 24

  7. ANSWER Scale of the map is1 : 24 = 1in : 24mi for Examples 4 and 5 GUIDED PRACTICE

  8. 14 in. measurement on model 560ft measurement on actual building xin. a. = 117.6 ft 560 x 1646.4 = x 2.94 = ANSWER 2.94 in. for Examples 4 and 5 GUIDED PRACTICE 5. What If ?Your friend has a model of the Reunion Tower that is 14 inches tall. What is the diameter of the dome on your friend’s model? SOLUTION Cross Products Property Solve for x.

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