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Scale Drawing Measurements

Grade 7 · Mathematics · Worksheet 2

  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, Liam uses a scale where 1 inch represents 3 feet. What is the area, in square inches, of the garden on his scale drawing?
    Answer: ______________
  2. Liam is creating a scale drawing of his school garden for a project. The actual garden is a rectangle measuring 48 feet by 36 feet. On his drawing, he uses a scale where 1 inch represents 8 feet. What is the perimeter, in inches, of the garden on his scale drawing?
    Answer: ______________
  3. A scale drawing uses 1 cm : 120 m. If a park measures 7.5 cm on the drawing, what is its actual length in meters? Answer: ______________
  4. A scale drawing uses 1 cm : 27 m. If a building is 12.7 cm tall on the drawing, what is its actual height in meters? Answer: ______________
  5. A scale drawing uses 1 cm = 25 m. If a building is 8.4 cm long on the drawing, what is its actual length in meters? Answer: ______________
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Answer Key & Explanations

Scale Drawing Measurements · Grade 7 · Worksheet 2

  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, Liam uses a scale where 1 inch represents 3 feet. What is the area, in square inches, of the garden on his scale drawing? Answer: 48 Solution: Find the dimensions of the garden in the scale drawing. The actual garden is 24 feet by 18 feet. The scale is 1 inch = 3 feet.
    Full step-by-step solution

    Step 1: Find the dimensions of the garden in the scale drawing. The actual garden is 24 feet by 18 feet. The scale is 1 inch = 3 feet. To find the drawing length in inches, divide each actual dimension by 3: Length in drawing = 24 feet ÷ 3 feet/inch = 8 inches Width in drawing = 18 feet ÷ 3 feet/inch = 6 inches Step 2: Find the area in the scale drawing. Area in drawing = length in inches × width in inches Area = 8 inches × 6 inches = 48 square inches Step 3: Conclusion The area of the garden on the scale drawing is 48 square inches.

  2. Liam is creating a scale drawing of his school garden for a project. The actual garden is a rectangle measuring 48 feet by 36 feet. On his drawing, he uses a scale where 1 inch represents 8 feet. What is the perimeter, in inches, of the garden on his scale drawing? Answer: 21 Solution: Find the actual perimeter of the garden. The actual garden is a rectangle 48 feet by 36 feet. Perimeter formula for a rectangle: P = 2 × (length + width) So, P = 2 × (48 + 36) = 2 × 84 = 168 feet.
    Full step-by-step solution

    Step 1: Find the actual perimeter of the garden. The actual garden is a rectangle 48 feet by 36 feet. Perimeter formula for a rectangle: P = 2 × (length + width) So, P = 2 × (48 + 36) = 2 × 84 = 168 feet. The actual perimeter is 168 feet. Step 2: Understand the scale. The scale is 1 inch on the drawing represents 8 feet in real life. That means: 1 inch = 8 feet. Step 3: Convert the actual perimeter from feet to inches on the drawing. We can use the scale directly on the perimeter because perimeter is a length, and the scale applies to all lengths. Scale: 1 inch (drawing) / 8 feet (actual). So, drawing perimeter = (actual perimeter in feet) × (1 inch / 8 feet) = 168 × (1/8) = 168 / 8 = 21 inches. Step 4: Conclusion. The perimeter of the garden on the scale drawing is 21 inches.

  3. A scale drawing uses 1 cm : 120 m. If a park measures 7.5 cm on the drawing, what is its actual length in meters? Answer: 900 Solution: Identify the scale: 1 cm on the drawing = 120 m in reality. The park's length on the drawing is 7.5 cm. Multiply the drawing length by the scale factor: 7.5 cm × 120 m/cm.
    Full step-by-step solution

    Step 1: Identify the scale: 1 cm on the drawing = 120 m in reality. Step 2: The park's length on the drawing is 7.5 cm. Step 3: Multiply the drawing length by the scale factor: 7.5 cm × 120 m/cm. Step 4: Calculate: 7.5 × 120 = 900. Step 5: The actual length is 900 meters.

  4. A scale drawing uses 1 cm : 27 m. If a building is 12.7 cm tall on the drawing, what is its actual height in meters? Answer: 342.9 Solution: The scale is 1 cm : 27 m, meaning 1 cm on the drawing equals 27 m in reality. The building's height on the drawing is 12.7 cm. Multiply the drawing measurement by the scale factor: 12.7 × 27.
    Full step-by-step solution

    Step 1: The scale is 1 cm : 27 m, meaning 1 cm on the drawing equals 27 m in reality. Step 2: The building's height on the drawing is 12.7 cm. Step 3: Multiply the drawing measurement by the scale factor: 12.7 × 27. Step 4: Calculate: 12.7 × 27 = 12.7 × (20 + 7) = 254 + 88.9 = 342.9. Step 5: The actual height is 342.9 meters.

  5. A scale drawing uses 1 cm = 25 m. If a building is 8.4 cm long on the drawing, what is its actual length in meters? Answer: 210 Solution: Identify the scale: 1 cm on the drawing = 25 m in reality The building measures 8.4 cm on the drawing Multiply the drawing length by the scale factor: 8.4 × 25 Calculate: 8.4 × 25 = 210 The actual length is 210 meters
    Full step-by-step solution

    Step 1: Identify the scale: 1 cm on the drawing = 25 m in reality Step 2: The building measures 8.4 cm on the drawing Step 3: Multiply the drawing length by the scale factor: 8.4 × 25 Step 4: Calculate: 8.4 × 25 = 210 Step 5: The actual length is 210 meters