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Grade 7 · Geometry · Worksheet 3

  1. A scale drawing of a rectangular garden uses a scale of 1 cm : 2.5 m. On the drawing, the garden measures 8 cm by 5 cm. What is the actual area of the garden in square meters?
    Answer: ______________
  2. A scale model of a rectangular swimming pool uses a scale of 1:150. On the model, the pool measures 12 cm by 8 cm. A similar rectangular hot tub is placed next to the pool. On the same model, the hot tub measures 3 cm by 2 cm. What is the actual area, in square meters, of the hot tub?
    Answer: ______________
  3. A scale drawing of a rectangular garden has dimensions 8 cm × 12 cm. If the scale is 1:200, what is the actual area of the garden in square meters? Answer: ______________
  4. Kai is using a map with a scale of 1 inch = 97 miles. On the map, Kai measures the distance between two cities as 2 inches. What is the actual distance in miles between the two cities? Answer: ______________
  5. A city planner is creating a scale model of a new rectangular park. The actual park measures 12,500 meters long by 8,000 meters wide. If the scale model uses a ratio of 1:250, what is the area of the model park in square meters? Answer: ______________
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Answer Key & Explanations

Similar Figures · Grade 7 · Worksheet 3

  1. A scale drawing of a rectangular garden uses a scale of 1 cm : 2.5 m. On the drawing, the garden measures 8 cm by 5 cm. What is the actual area of the garden in square meters? Answer: 250 Solution: The scale is 1 cm : 2.5 m. This means every 1 cm on the drawing represents 2.5 m in real life. On the drawing, the length is 8 cm.
    Full step-by-step solution

    Step 1: Understand the scale The scale is 1 cm : 2.5 m. This means every 1 cm on the drawing represents 2.5 m in real life. Step 2: Find the actual length On the drawing, the length is 8 cm. Actual length = 8 cm × 2.5 m/cm Actual length = 20 m. Step 3: Find the actual width On the drawing, the width is 5 cm. Actual width = 5 cm × 2.5 m/cm Actual width = 12.5 m. Step 4: Calculate the actual area Area of a rectangle = length × width Area = 20 m × 12.5 m Area = 250 square meters. Final answer: 250

  2. A scale model of a rectangular swimming pool uses a scale of 1:150. On the model, the pool measures 12 cm by 8 cm. A similar rectangular hot tub is placed next to the pool. On the same model, the hot tub measures 3 cm by 2 cm. What is the actual area, in square meters, of the hot tub? Answer: 13.5 Solution: Identify the scale factor. The model uses a scale of 1:150, meaning 1 cm on the model represents 150 cm in reality. Convert the scale to meters.
    Full step-by-step solution

    Step 1: Identify the scale factor. The model uses a scale of 1:150, meaning 1 cm on the model represents 150 cm in reality. Step 2: Convert the scale to meters. Since 150 cm = 1.5 m, 1 cm on the model represents 1.5 m in reality. Step 3: Find the actual dimensions of the hot tub. Length: 3 cm × 1.5 m/cm = 4.5 m. Width: 2 cm × 1.5 m/cm = 3 m. Step 4: Calculate the actual area. Area = length × width = 4.5 m × 3 m = 13.5 square meters. The answer is 13.5.

  3. A scale drawing of a rectangular garden has dimensions 8 cm × 12 cm. If the scale is 1:200, what is the actual area of the garden in square meters? Answer: 384 Solution: The scale is 1:200, which means 1 cm on the drawing represents 200 cm in real life.
    Full step-by-step solution

    Step 1: Understand the scale The scale is 1:200, which means 1 cm on the drawing represents 200 cm in real life. Step 2: Find the actual dimensions in centimeters Length on drawing = 12 cm Actual length = 12 × 200 = 2400 cm Width on drawing = 8 cm Actual width = 8 × 200 = 1600 cm Step 3: Convert centimeters to meters Since 1 m = 100 cm: Actual length in meters = 2400 / 100 = 24 m Actual width in meters = 1600 / 100 = 16 m Step 4: Calculate the actual area Area = length × width Area = 24 × 16 Step 5: Perform the multiplication 24 × 16 = 24 × (10 + 6) = 24 × 10 + 24 × 6 = 240 + 144 = 384 So, the actual area of the garden is 384 square meters.

  4. Kai is using a map with a scale of 1 inch = 97 miles. On the map, Kai measures the distance between two cities as 2 inches. What is the actual distance in miles between the two cities? Answer: 194 Solution: The scale means every 1 inch on the map represents 97 miles in real life. The map distance is 2 inches, so the actual distance is 2 × 97 = 194 miles. The actual distance between the cities is 194 miles.
    Full step-by-step solution

    Step 1: The scale means every 1 inch on the map represents 97 miles in real life. Step 2: The map distance is 2 inches, so the actual distance is 2 × 97 = 194 miles. Step 3: The actual distance between the cities is 194 miles.

  5. A city planner is creating a scale model of a new rectangular park. The actual park measures 12,500 meters long by 8,000 meters wide. If the scale model uses a ratio of 1:250, what is the area of the model park in square meters? Answer: 1600 Solution: The scale is 1:250. This means 1 unit on the model represents 250 units in reality.
    Full step-by-step solution

    Let's go step-by-step. --- **Step 1: Understand the scale ratio** The scale is 1:250. This means 1 unit on the model represents 250 units in reality. --- **Step 2: Find model length and width** Actual length = 12,500 m Model length = Actual length ÷ 250 Model length = 12,500 / 250 = 50 m Actual width = 8,000 m Model width = Actual width ÷ 250 Model width = 8,000 / 250 = 32 m --- **Step 3: Calculate model area** Model area = Model length × Model width Model area = 50 m × 32 m = 1600 m² --- **Step 4: Important note** We did not calculate the actual park area and then divide by 250² directly, but we can check: Actual area = 12,500 × 8,000 = 100,000,000 m² Scale for area = (1:250)² = 1:62,500 Model area = 100,000,000 / 62,500 = 1600 m² ✅ Both methods give the same result. --- **Final answer: 1600**