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Grade 7 · Geometry · Worksheet 2

  1. A rectangular garden measures 18 m by 12 m. A scale drawing uses a scale of 1:150. What is the area of the garden in the scale drawing in cm²?
    Answer: ______________
  2. Emma is creating a scale drawing of her school's rectangular library for a class project. The actual library measures 45 meters by 30 meters. She wants her drawing to fit on a standard sheet of paper, so she decides to use a scale where 1 centimeter represents 5 meters. What will be the dimensions of her scale drawing in centimeters?
    Answer: ______________
  3. Emma is creating a scale drawing of her neighborhood park for a community project. The actual park has a rectangular playground that measures 45 meters by 30 meters. She wants to fit her drawing on a standard poster board that is 60 centimeters wide. If she uses the entire width of the poster board for the longer side of the playground, what scale factor is she using for her drawing?
    Answer: ______________
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Answer Key & Explanations

Similar Figures · Grade 7 · Worksheet 2

  1. A rectangular garden measures 18 m by 12 m. A scale drawing uses a scale of 1:150. What is the area of the garden in the scale drawing in cm²? Answer: 96 Solution: The scale is 1:150. This means 1 unit on the drawing represents 150 units in reality. Both length and width will be scaled down by the factor 150.
    Full step-by-step solution

    Let's go step-by-step. --- **Step 1: Understand the scale** The scale is 1:150. This means 1 unit on the drawing represents 150 units in reality. Both length and width will be scaled down by the factor 150. --- **Step 2: Convert real garden dimensions to cm** Real length = 18 m Real width = 12 m 1 m = 100 cm, so: Length in cm = 18 × 100 = 1800 cm Width in cm = 12 × 100 = 1200 cm --- **Step 3: Apply the scale to find drawing dimensions in cm** Scale factor (from real to drawing) = 1/150. Drawing length = 1800 cm × (1/150) = 1800 / 150 = 12 cm Drawing width = 1200 cm × (1/150) = 1200 / 150 = 8 cm --- **Step 4: Find the area in the drawing** Area in drawing = length in drawing × width in drawing = 12 cm × 8 cm = 96 cm² --- **Step 5: Conclusion** The area of the garden in the scale drawing is 96 cm². --- **Final answer:** 96

  2. Emma is creating a scale drawing of her school's rectangular library for a class project. The actual library measures 45 meters by 30 meters. She wants her drawing to fit on a standard sheet of paper, so she decides to use a scale where 1 centimeter represents 5 meters. What will be the dimensions of her scale drawing in centimeters? Answer: 9 cm by 6 cm Solution: The scale is 1 cm : 5 m, meaning each centimeter in the drawing represents 5 meters in real life. For the length: 45 m ÷ 5 m/cm = 9 cm For the width: 30 m ÷ 5 m/cm = 6 cm The scale drawing dimensions are 9 cm by 6 cm.
    Full step-by-step solution

    Step 1: The scale is 1 cm : 5 m, meaning each centimeter in the drawing represents 5 meters in real life. Step 2: For the length: 45 m ÷ 5 m/cm = 9 cm Step 3: For the width: 30 m ÷ 5 m/cm = 6 cm Step 4: The scale drawing dimensions are 9 cm by 6 cm.

  3. Emma is creating a scale drawing of her neighborhood park for a community project. The actual park has a rectangular playground that measures 45 meters by 30 meters. She wants to fit her drawing on a standard poster board that is 60 centimeters wide. If she uses the entire width of the poster board for the longer side of the playground, what scale factor is she using for her drawing? Answer: 1:75 Solution: Convert the actual playground length to centimeters 45 meters = 45 × 100 = 4500 centimeters The drawing uses 60 centimeters to represent the actual 4500 centimeters Find the scale factor by comparing drawing length to actual length Scale factor = drawing length : actual length = 60 : 4500 Divide…
    Full step-by-step solution

    Step 1: Convert the actual playground length to centimeters 45 meters = 45 × 100 = 4500 centimeters Step 2: The drawing uses 60 centimeters to represent the actual 4500 centimeters Step 3: Find the scale factor by comparing drawing length to actual length Scale factor = drawing length : actual length = 60 : 4500 Step 4: Simplify the ratio Divide both sides by 60: 60 ÷ 60 = 1, 4500 ÷ 60 = 75 So the scale factor is 1:75 The answer is 1:75.