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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, he uses a scale where 1 inch represents 4 feet. What is the area, in square inches, of the garden on his scale drawing?
    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. Emma is creating a scale drawing of her neighborhood park for a community project. The actual park is a rectangle measuring 240 meters by 180 meters. On her drawing, she uses a scale where 1 centimeter represents 30 meters. What is the area, in square centimeters, of the park on her scale drawing?
    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. A scale drawing uses 1:500. If a building is 8 cm tall on the drawing, what is its actual height in meters? 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, he uses a scale where 1 inch represents 4 feet. What is the area, in square inches, of the garden on his scale drawing? Answer: 27 Solution: First, find the dimensions of the garden in the scale drawing. The actual length is 24 feet. The scale is 1 inch = 4 feet.
    Full step-by-step solution

    First, find the dimensions of the garden in the scale drawing. The actual length is 24 feet. The scale is 1 inch = 4 feet. So, the length in the drawing = (24 feet) / (4 feet per inch) = 24 / 4 = 6 inches. The actual width is 18 feet. The width in the drawing = (18 feet) / (4 feet per inch) = 18 / 4 = 4.5 inches. Now, the area in the drawing is length × width in inches. Area = 6 inches × 4.5 inches. Multiply: 6 × 4.5 = 27. So, the area of the garden on the scale drawing is 27 square 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. Emma is creating a scale drawing of her neighborhood park for a community project. The actual park is a rectangle measuring 240 meters by 180 meters. On her drawing, she uses a scale where 1 centimeter represents 30 meters. What is the area, in square centimeters, of the park on her scale drawing? Answer: 48 Solution: Actual length = 240 meters Scale: 1 cm = 30 meters Drawing length = 240 ÷ 30 = 8 cm Actual width = 180 meters Drawing width = 180 ÷ 30 = 6 cm Area = length × width = 8 cm × 6 cm = 48 square cm The answer is 48 square centimeters.
    Full step-by-step solution

    Step 1: Find the length on the drawing Actual length = 240 meters Scale: 1 cm = 30 meters Drawing length = 240 ÷ 30 = 8 cm Step 2: Find the width on the drawing Actual width = 180 meters Drawing width = 180 ÷ 30 = 6 cm Step 3: Calculate the area on the drawing Area = length × width = 8 cm × 6 cm = 48 square cm The answer is 48 square 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. A scale drawing uses 1:500. If a building is 8 cm tall on the drawing, what is its actual height in meters? Answer: 40 Solution: The scale is 1:500, meaning 1 cm on the drawing represents 500 cm in reality. The building is 8 cm tall on the drawing, so actual height = 8 × 500 = 4000 cm. Convert centimeters to meters: 4000 cm ÷ 100 = 40 m.
    Full step-by-step solution

    Step 1: The scale is 1:500, meaning 1 cm on the drawing represents 500 cm in reality. Step 2: The building is 8 cm tall on the drawing, so actual height = 8 × 500 = 4000 cm. Step 3: Convert centimeters to meters: 4000 cm ÷ 100 = 40 m. The actual height of the building is 40 meters.