Pre-Algebra
Geometry
Scale drawings and geometric figures
20 practice questions
0 video lessons
Theory + worked examples
Scale Drawings and Geometric Figures
Texas Pre-Algebra (TEKS) • Standard 7.5(C) • Geometry
Scale Drawings and Geometric Figures is a topic in Geometry in the Texas Essential Knowledge and Skills. It is aligned to Standard 7.5(C), which requires students to solve problems involving scale drawings of geometric figures.
A scale drawing reproduces a figure at a different size; all lengths multiply by the scale factor while the shape stays the same.
Theory
A scale drawing reproduces a figure with all lengths multiplied by the scale factor; the shape is unchanged.
Area scales by the square of the scale factor.
A figure enlarged by \(2\).
Scale drawings.
Scaling:
\[\text{new length}=\text{scale factor}\times\text{old length}\]
Area scales by the factor squared.
How to use a scale drawing
- Find the scale factor.
- Multiply lengths to enlarge, divide to reduce.
- Keep the shape the same.
- Square the factor for area.
Example 1 — New length
A \(3\)-cm side is drawn at scale factor \(4\). Find the new length.
Solution
Multiply.
| \(3\cdot4\) | \(=\) | \(12\text{ cm}\) |
Example 2 — Scale factor
A \(2\)-in model becomes \(10\) in. Find the scale factor.
Solution
Divide.
| \(\dfrac{10}{2}\) | \(=\) | \(5\) |
Example 3 — Area
How does area change with scale factor \(3\)?
Solution
Area scales by the square.
| \(3^2\) | \(=\) | \(9\text{ times}\) |
Example 4 — Reduce
A \(12\)-ft wall at scale \(1:4\) is how long?
Solution
Divide by \(4\).
| \(\dfrac{12}{4}\) | \(=\) | \(3\text{ ft}\) |
Common pitfalls
Area scales by the square, not the factor itself.
All lengths use the same factor.
The shape stays similar.
Frequently asked questions
What is a scale drawing?
A figure reproduced at a different size.
How do lengths change?
Multiply by the scale factor.
How does area change?
By the factor squared.
Does the shape change?
No.
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