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Question

Difficulty: MediumScale Drawings

A contractor is analyzing a zoning plan for a commercial parking lot. The plan's legend indicates a scale of 1 inch=10 yards1\text{ inch} = 10\text{ yards}. If the parking lot covers an area of 4 square inches4\text{ square inches} on the zoning plan, what is the actual area of the parking lot in square feet?

  1. A
    120120
  2. B
    400400
  3. C
    1,2001,200
  4. 3,6003,600Answer

Answer

The actual area of the parking lot is 3,6003,600 square feet.
The correct answer is found by first aligning the units: the scale of 1 inch=10 yards1\text{ inch} = 10\text{ yards} is equivalent to 1 inch=30 feet1\text{ inch} = 30\text{ feet}. Because we are dealing with area (a two-dimensional measurement), this linear scale must be squared, meaning 1 square inch1\text{ square inch} on the drawing represents 900 square feet900\text{ square feet} in reality (302=90030^2 = 900). Finally, multiplying the drawing's area by this factor yields the actual area: 4×900=3,600 square feet4 \times 900 = 3,600\text{ square feet}.

Step-by-Step Solution

1
Convert the linear scale from yards to feet.
10 yards=30 feet10\text{ yards} = 30\text{ feet}, so the scale is 1 inch=30 feet1\text{ inch} = 30\text{ feet}.
The final question asks for the area in square feet, so it is easiest to align the units of the scale factor first.
2
Determine the area scale factor by squaring the linear scale.
1 square inch=(30 feet)×(30 feet)=900 square feet1\text{ square inch} = (30\text{ feet}) \times (30\text{ feet}) = 900\text{ square feet}.
Because area represents two dimensions, the linear scale must be squared to find out how much actual area one square inch on the drawing represents.
3
Multiply the drawing area by the area scale factor.
4 square inches×900 square feet per square inch=3,600 square feet4\text{ square inches} \times 900\text{ square feet per square inch} = 3,600\text{ square feet}.
This scales the blueprint measurement up to the actual real-world area.

Key Concept

When using a scale drawing to find a real-world area, the linear scale factor must be squared. Furthermore, all units must be carefully tracked and converted to match the requested final unit.
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Topics

Scale Drawings

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