Key takeaway: A scale drawing is a flat picture of a real object or place in which every length is the actual length multiplied by the same ratio, called the scale.
Grade 77.G.A.1Geometry and Measurement
Definition of Scale Drawing
A scale drawing shows something too large or too small to draw at full size, such as a house, a map or a watch gear. The shape is identical to the real thing, but all lengths are shrunk or enlarged by one fixed ratio.
That ratio is written on the drawing as the scale, for example \(1\text{ in} : 4\text{ ft}\). Every inch on the paper stands for 4 feet in the real room. Angles never change, because only lengths are scaled. Architects, mapmakers and model-car designers all depend on this idea.
Formula and notation
A scale compares a drawing length to the actual length, and the two quantities form a proportion:
\[\frac{\text{drawing length}}{\text{actual length}} = \frac{1\text{ in}}{4\text{ ft}}\]
Solve for the missing length with cross multiplication or by multiplying by the scale.
Key facts
- Every scale drawing keeps angles: the picture angles equal the matching angles in the real object.
- Area does not follow the length scale; it changes by the square of that scale.
- A scale with units on both sides, like 1 cm : 50 m, needs no conversion until you compare.
- A bigger drawing length per real unit means a larger picture.
Scale Drawing example
A bedroom is shown in a scale drawing with the scale 1 inch : 4 feet. On the plan the room measures 3.5 inches by 2.75 inches. Find the real length, width and floor area.
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Length: \(3.5 \times 4 = 14\) feet.
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Width: \(2.75 \times 4 = 11\) feet.
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Area: \(14 \times 11 = 154\) square feet.
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Check: the drawing’s area is \(3.5 \times 2.75 = 9.625\) square inches, and \(9.625 \times 16 = 154\).
The room is 14 ft by 11 ft with a floor area of 154 square feet.
Common mistake
Watch out
Wen finds the area on the scale drawing, 9.625 square inches, and multiplies by 4 to get 38.5 square feet for the bedroom.
Why it is wrong
The scale 1 : 4 applies to lengths, and area has two lengths multiplied together. Each of them grows by 4, so the area grows by \(4 \times 4 = 16\). Correct: \(9.625 \times 16 = 154\) square feet. Multiply the lengths first, then find the area.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Geometry and Measurement