Scale Drawing Measurements

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Scale Drawing Measurements · Grade 7 · Worksheet 2

1. A scale drawing of a rectangular garden uses a scale of 1:500. On the drawing, the garden measures 8 cm by 12 cm. What is the actual area of the garden in square meters? Answer: 2400 Solution: The scale is 1:500, which means 1 cm on the drawing represents 500 cm in real life.
   Full step-by-step solution

   Let's go step-by-step. Step 1: Understand the scale The scale is 1:500, which means 1 cm on the drawing represents 500 cm in real life. Step 2: Find actual dimensions in cm Length on drawing = 12 cm Actual length = 12 × 500 = 6000 cm Width on drawing = 8 cm Actual width = 8 × 500 = 4000 cm Step 3: Convert cm to meters Since 1 m = 100 cm: Actual length in meters = 6000 / 100 = 60 m Actual width in meters = 4000 / 100 = 40 m Step 4: Calculate actual area Area = length × width = 60 × 40 = 2400 square meters Thus, the actual area of the garden is 2400 square meters.

2. A map has a scale of 1:40000. Hana measures the distance between two towns on the map as 12.6 cm. What is the actual distance in kilometers? Answer: 5.04 Solution: The scale 1:40000 means 1 cm on the map = 40000 cm in reality. Map distance = 12.6 cm. Actual distance in cm = 12.6 × 40000 = 504000 cm.
   Full step-by-step solution

   Step 1: The scale 1:40000 means 1 cm on the map = 40000 cm in reality. Step 2: Map distance = 12.6 cm. Step 3: Actual distance in cm = 12.6 × 40000 = 504000 cm. Step 4: Convert cm to km: 1 km = 100000 cm, so 504000 ÷ 100000 = 5.04 km. The answer is 5.04.

3. A map has a scale of 1:50000. If two landmarks are 6.2 cm apart on the map, what is the actual distance in kilometers? Answer: 3.1 Solution: The scale is 1:50000, which means 1 cm on the map represents 50000 cm in actual distance.
   Full step-by-step solution

   Step 1: The scale is 1:50000, which means 1 cm on the map represents 50000 cm in actual distance. Step 2: Multiply the map distance by the scale factor: 6.2 cm × 50000 = 310000 cm Step 3: Convert centimeters to meters: 310000 cm ÷ 100 = 3100 m Step 4: Convert meters to kilometers: 3100 m ÷ 1000 = 3.1 km The actual distance between the landmarks is 3.1 kilometers.

4. Liam is creating a scale drawing of his rectangular backyard for a landscaping project. The actual dimensions of the yard are 60 feet by 45 feet. On his drawing, he uses a scale where 1 inch represents 15 feet. What is the area, in square inches, of the backyard on his scale drawing? Answer: 12 Solution: The scale is 1 inch on the drawing = 15 feet in real life. So, to convert actual feet to drawing inches, divide by 15. Find the drawing dimensions in inches.
   Full step-by-step solution

   Step 1: Understand the scale. The scale is 1 inch on the drawing = 15 feet in real life. So, to convert actual feet to drawing inches, divide by 15. Step 2: Find the drawing dimensions in inches. Actual length = 60 feet. Drawing length = 60 / 15 = 4 inches. Actual width = 45 feet. Drawing width = 45 / 15 = 3 inches. Step 3: Find the area on the drawing. Area in drawing = length in inches × width in inches. Area = 4 × 3 = 12 square inches. Step 4: Conclusion. The area of the backyard on the scale drawing is 12 square inches.

5. 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.

6. A scale drawing of a triangular garden uses a scale of 1 cm : 15 m. In the drawing, the triangle has a base of 6.8 cm and a height of 4.5 cm. What is the actual area of the garden in square meters? Answer: 3442.5 Solution: Scale: 1 cm = 15 m Drawing base = 6.8 cm Actual base = 6.8 × 15 = 102 m Drawing height = 4.5 cm Actual height = 4.5 × 15 = 67.5 m Calculate the actual area of the triangular garden Area of triangle = (base × height) ÷ 2 Area = (102 × 67.5) ÷ 2 Area = (6885) ÷ 2 Area = 3442.5 square meters The…
   Full step-by-step solution

   Step 1: Calculate the actual base length Scale: 1 cm = 15 m Drawing base = 6.8 cm Actual base = 6.8 × 15 = 102 m Step 2: Calculate the actual height Drawing height = 4.5 cm Actual height = 4.5 × 15 = 67.5 m Step 3: Calculate the actual area of the triangular garden Area of triangle = (base × height) ÷ 2 Area = (102 × 67.5) ÷ 2 Area = (6885) ÷ 2 Area = 3442.5 square meters The actual area of the garden is 3442.5 square meters.

7. Mia is designing a floor plan for a tiny house. The scale is 1:16. In the drawing, the width of the living room is 24 cm. What is the actual width of the living room in centimeters? Answer: 384 Solution: Interpret the scale: 1 cm in the drawing = 16 cm in the real house. Multiply the drawing width by the scale factor: 24 × 16 = 384. The actual width of the living room is 384 centimeters.
   Full step-by-step solution

   Step 1: Interpret the scale: 1 cm in the drawing = 16 cm in the real house. Step 2: Multiply the drawing width by the scale factor: 24 × 16 = 384. The actual width of the living room is 384 centimeters.