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Scale Drawing Measurements

Grade 7 · Mathematics · Worksheet 1

  1. A map has a scale of 1:25000. If two towns are 8 cm apart on the map, what is the actual distance in kilometers? Answer: ______________
  2. Liam is creating a scale drawing of his rectangular garden for a landscaping project. On his drawing, which uses a scale of 1:150, the garden measures 8 cm by 12 cm. What is the actual area of Liam's garden in square meters?
    Answer: ______________
  3. Emma is designing a scale model of a new community park for her city planning project. The actual park will be a rectangle measuring 240 meters by 180 meters. Her model uses a scale where 1 centimeter represents 15 meters. What will be the perimeter of Emma's scale model in centimeters?
    Answer: ______________
  4. A scale drawing uses 1:500. If a building measures 8.4 cm on the drawing, what is the actual length in meters? Answer: ______________
  5. Sophia is building a model airplane. The model is built using a scale of 1:15. If the actual wingspan of the real airplane is 1455 centimeters, what is the length of the wingspan on Sophia's model in centimeters? Answer: ______________
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Answer Key & Explanations

Scale Drawing Measurements · Grade 7 · Worksheet 1

  1. A map has a scale of 1:25000. If two towns are 8 cm apart on the map, what is the actual distance in kilometers? Answer: 2 Solution: A scale of 1:25000 means that 1 cm on the map represents 25000 cm in real life. Find the actual distance in centimeters. The towns are 8 cm apart on the map.
    Full step-by-step solution

    Step 1: Understand the scale. A scale of 1:25000 means that 1 cm on the map represents 25000 cm in real life. Step 2: Find the actual distance in centimeters. The towns are 8 cm apart on the map. Actual distance in cm = 8 × 25000 = 200000 cm. Step 3: Convert centimeters to meters. We know 1 m = 100 cm. So, actual distance in meters = 200000 / 100 = 2000 m. Step 4: Convert meters to kilometers. We know 1 km = 1000 m. So, actual distance in km = 2000 / 1000 = 2 km. Final answer: The actual distance between the towns is 2 km.

  2. Liam is creating a scale drawing of his rectangular garden for a landscaping project. On his drawing, which uses a scale of 1:150, the garden measures 8 cm by 12 cm. What is the actual area of Liam's garden in square meters? Answer: 216 Solution: The scale is 1:150, meaning 1 cm on the drawing represents 150 cm in real life.
    Full step-by-step solution

    Let's go step by step. --- **Step 1: Understand the scale** The scale is 1:150, meaning 1 cm on the drawing represents 150 cm in real life. --- **Step 2: Find the actual dimensions in cm** Drawing length = 12 cm Actual length = 12 × 150 = 1800 cm Drawing width = 8 cm Actual width = 8 × 150 = 1200 cm So actual garden size: 1800 cm by 1200 cm. --- **Step 3: Convert cm to meters** 1 m = 100 cm, so: Length in meters = 1800 / 100 = 18 m Width in meters = 1200 / 100 = 12 m --- **Step 4: Calculate actual area** Area = length × width Area = 18 × 12 = 216 square meters. --- **Final answer:** 216

  3. Emma is designing a scale model of a new community park for her city planning project. The actual park will be a rectangle measuring 240 meters by 180 meters. Her model uses a scale where 1 centimeter represents 15 meters. What will be the perimeter of Emma's scale model in centimeters? Answer: 56 Solution: Actual length = 240 meters Scale: 1 cm = 15 meters Scaled length = 240 ÷ 15 = 16 cm Actual width = 180 meters Scale: 1 cm = 15 meters Scaled width = 180 ÷ 15 = 12 cm Perimeter = 2 × (length + width) Perimeter = 2 × (16 + 12) Perimeter = 2 × 28 Perimeter = 56 cm The perimeter of Emma's scale…
    Full step-by-step solution

    Step 1: Find the scaled length Actual length = 240 meters Scale: 1 cm = 15 meters Scaled length = 240 ÷ 15 = 16 cm Step 2: Find the scaled width Actual width = 180 meters Scale: 1 cm = 15 meters Scaled width = 180 ÷ 15 = 12 cm Step 3: Calculate the perimeter of the scaled model Perimeter = 2 × (length + width) Perimeter = 2 × (16 + 12) Perimeter = 2 × 28 Perimeter = 56 cm The perimeter of Emma's scale model is 56 centimeters.

  4. A scale drawing uses 1:500. If a building measures 8.4 cm on the drawing, what is the actual length in meters? Answer: 42 Solution: The scale is 1:500, which means 1 cm on the drawing represents 500 cm in actual length. Multiply the drawing measurement by the scale factor: 8.4 cm × 500 = 4200 cm.
    Full step-by-step solution

    Step 1: The scale is 1:500, which means 1 cm on the drawing represents 500 cm in actual length. Step 2: Multiply the drawing measurement by the scale factor: 8.4 cm × 500 = 4200 cm. Step 3: Convert centimeters to meters by dividing by 100: 4200 cm ÷ 100 = 42 m. The actual length of the building is 42 meters.

  5. Sophia is building a model airplane. The model is built using a scale of 1:15. If the actual wingspan of the real airplane is 1455 centimeters, what is the length of the wingspan on Sophia's model in centimeters? Answer: 97 Solution: Identify the scale: The real airplane is 15 times larger than the model. Divide the actual wingspan by the scale factor: 1455 ÷ 15 = 97. The wingspan on the model is 97 centimeters.
    Full step-by-step solution

    Step 1: Identify the scale: The real airplane is 15 times larger than the model. Step 2: Divide the actual wingspan by the scale factor: 1455 ÷ 15 = 97. The wingspan on the model is 97 centimeters.