Scale Drawing
In short: Scale drawing means a picture of a real object, shrunk or stretched so that each length on paper is the real length multiplied by one fixed ratio, which keeps the shape unchanged.
7th GradeGeometry7.G.A.1
What is Scale Drawing?
No architect can sketch a house at full size, so a scale drawing shrinks every real length by one fixed ratio, such as 1 inch of paper for every 8 feet of building.
With the ratio constant everywhere, angles survive and lengths stay proportional. Real length equals paper length times the scale, and an area grows by the square of that scale. Measuring the picture therefore tells you the true dimensions.
How to spot it
- A floor plan, blueprint or map carries a note such as 1 in = 8 ft or 1 cm : 25 km.
- You measure a length on paper and must report the length in the real world, or go the other way.
- A model car, building or bridge is described by how much smaller it is than the original.
- Pictured lengths must be turned into a real perimeter or floor area.
The method
- State the scale as paper length to real length, keeping the units matched.
- Build a proportion that holds the known length and the unknown length.
- Multiply or divide to reach the missing length, converting units afterward if needed.
- For floor space, recover the real side lengths first and multiply those, rather than scaling the area itself.
Scale Drawing: solved example
Problem
A school architect draws a gym storage room on a plan with the scale \(1\text{ in} = 8\text{ ft}\). On paper it measures 5.5 inches by 3 inches. What are the real dimensions and the real floor area?
Solution
Width: \(5.5 \times 8 = 44\) feet. Length: \(3 \times 8 = 24\) feet.
Area: \(44 \times 24 = 1{,}056\) square feet. The room is 44 ft by 24 ft with an area of 1,056 square feet.
Try it
Question 1
On a regional map, 1 cm stands for 25 km. Two towns are 7.2 cm apart. How far apart are they?
Show the answer
\(7.2 \times 25 = 180\) km.
Question 2
A sailboat measures 15 ft from bow to stern. How many inches is that on a plan drawn with \(1\text{ in} = 2.5\text{ ft}\)?
Show the answer
\(15 \div 2.5 = 6\) inches.
Scale Drawing vs. Scale Factor
A scale drawing is the finished picture or plan. The scale factor is the single number that links it to the real object, such as 8 feet per inch or one ninety-sixth when both are in inches. Tools like a map key state the scale; you calculate with the factor.
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