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Scale Drawing Measurements

Grade 7 · Mathematics · Worksheet 3

  1. Liam is creating a scale drawing of his rectangular garden for a landscaping project. The actual garden measures 24 feet by 18 feet. On his drawing, the length is represented by 8 inches. Using the same scale, what is the width of the garden on the drawing, in inches?
    Answer: ______________
  2. A scale drawing uses 1:500. If a building measures 3.2 cm on the drawing, what is the actual length in meters? Answer: ______________
  3. A scale drawing uses 1 cm : 27 m. If a building measures 12.7 cm on the drawing, what is its actual height in meters? Answer: ______________
  4. Emma is creating a scale model of a new city park for her urban planning project. The actual park is rectangular and measures 240 meters by 180 meters. On her model, she uses a scale of 1:1200. What is the area of the park in her scale model in square centimeters?
    Answer: ______________
  5. Ethan is building a model airplane. The model is built using a scale of 1:16. If the actual wingspan of the real airplane is 2752 centimeters, what is the length of the wingspan on Ethan's model in centimeters? Answer: ______________
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Answer Key & Explanations

Scale Drawing Measurements · Grade 7 · Worksheet 3

  1. Liam is creating a scale drawing of his rectangular garden for a landscaping project. The actual garden measures 24 feet by 18 feet. On his drawing, the length is represented by 8 inches. Using the same scale, what is the width of the garden on the drawing, in inches? Answer: 6 Solution: First, identify the scale used in the drawing. The actual length of the garden is 24 feet, and it is represented as 8 inches on the drawing. 8 inches in drawing = 24 feet in reality.
    Full step-by-step solution

    First, identify the scale used in the drawing. The actual length of the garden is 24 feet, and it is represented as 8 inches on the drawing. So, the scale is: 8 inches in drawing = 24 feet in reality. We can write the scale as a ratio: Scale = (drawing length in inches) / (actual length in feet) Scale = 8 inches / 24 feet. Simplify that fraction: 8/24 = 1/3. So the scale is: 1 inch on the drawing = 3 feet in reality. Now, the actual width of the garden is 18 feet. We want the drawing width in inches. Using the scale: Drawing width (inches) / Actual width (feet) = 1 inch / 3 feet. So, Drawing width = (Actual width in feet) × (1 inch / 3 feet). Substitute the actual width: Drawing width = 18 × (1/3) Drawing width = 18/3 Drawing width = 6 inches. Thus, the width on the drawing is 6 inches.

  2. A scale drawing uses 1:500. If a building measures 3.2 cm on the drawing, what is the actual length in meters? Answer: 16 Solution: Identify the scale ratio: 1:500 means 1 cm on drawing = 500 cm in reality Multiply drawing measurement by scale factor: 3.2 cm × 500 = 1600 cm Convert centimeters to meters: 1600 cm ÷ 100 = 16 m The actual length is 16 meters.
    Full step-by-step solution

    Step 1: Identify the scale ratio: 1:500 means 1 cm on drawing = 500 cm in reality Step 2: Multiply drawing measurement by scale factor: 3.2 cm × 500 = 1600 cm Step 3: Convert centimeters to meters: 1600 cm ÷ 100 = 16 m Step 4: The actual length is 16 meters.

  3. A scale drawing uses 1 cm : 27 m. If a building measures 12.7 cm on the drawing, what is its actual height in meters? Answer: 342.9 Solution: The scale is 1 cm = 27 m. Step 2: The drawing measurement is 12.7 cm. Step 3: Multiply 12.7 by 27 to find the actual height.
    Full step-by-step solution

    Step 1: The scale is 1 cm = 27 m. Step 2: The drawing measurement is 12.7 cm. Step 3: Multiply 12.7 by 27 to find the actual height. Step 4: 12.7 × 27 = 342.9. Step 5: The actual height is 342.9 meters.

  4. Emma is creating a scale model of a new city park for her urban planning project. The actual park is rectangular and measures 240 meters by 180 meters. On her model, she uses a scale of 1:1200. What is the area of the park in her scale model in square centimeters? Answer: 300 Solution: Convert the actual dimensions from meters to centimeters Actual length: 240 m × 100 = 24,000 cm Actual width: 180 m × 100 = 18,000 cm Apply the scale factor of 1:1200 to find model dimensions Model length: 24,000 cm ÷ 1200 = 20 cm Model width: 18,000 cm ÷ 1200 = 15 cm Area = length × width = 20…
    Full step-by-step solution

    Step 1: Convert the actual dimensions from meters to centimeters Actual length: 240 m × 100 = 24,000 cm Actual width: 180 m × 100 = 18,000 cm Step 2: Apply the scale factor of 1:1200 to find model dimensions Model length: 24,000 cm ÷ 1200 = 20 cm Model width: 18,000 cm ÷ 1200 = 15 cm Step 3: Calculate the area of the model Area = length × width = 20 cm × 15 cm = 300 cm² The answer is 300 square centimeters.

  5. Ethan is building a model airplane. The model is built using a scale of 1:16. If the actual wingspan of the real airplane is 2752 centimeters, what is the length of the wingspan on Ethan's model in centimeters? Answer: 172 Solution: Identify the scale: The real airplane is 16 times larger than the model. Divide the actual wingspan by the scale factor: 2752 ÷ 16 = 172. The wingspan on the model is 172 centimeters.
    Full step-by-step solution

    Step 1: Identify the scale: The real airplane is 16 times larger than the model. Step 2: Divide the actual wingspan by the scale factor: 2752 ÷ 16 = 172. The wingspan on the model is 172 centimeters.