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Grade 7 · Geometry · Worksheet 1

  1. 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: ______________
  2. Liam is designing a scale model of a new playground for his city. The actual playground will be a rectangular area measuring 120 meters by 90 meters. Liam's blueprint uses a scale where 1 centimeter represents 15 meters. What will be the perimeter of the playground on his blueprint, in centimeters?
    Answer: ______________
  3. 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: ______________
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Answer Key & Explanations

Similar Figures · Grade 7 · Worksheet 1

  1. 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.

  2. Liam is designing a scale model of a new playground for his city. The actual playground will be a rectangular area measuring 120 meters by 90 meters. Liam's blueprint uses a scale where 1 centimeter represents 15 meters. What will be the perimeter of the playground on his blueprint, in centimeters? Answer: 28 Solution: The scale is 1 cm on the blueprint represents 15 meters in reality.
    Full step-by-step solution

    Step 1: Understand the scale The scale is 1 cm on the blueprint represents 15 meters in reality. Step 2: Find the blueprint dimensions Actual length = 120 m Blueprint length = 120 / 15 = 8 cm Actual width = 90 m Blueprint width = 90 / 15 = 6 cm Step 3: Recall the formula for perimeter of a rectangle Perimeter = 2 × (length + width) Step 4: Apply the formula to blueprint dimensions Perimeter on blueprint = 2 × (8 cm + 6 cm) = 2 × (14 cm) = 28 cm Step 5: Final answer The perimeter on the blueprint is 28 cm.

  3. 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.