Similar Figures Proportion Calculator

Proportion Formula:

\[ \frac{a_1}{a_2} = \frac{b_1}{b_2} \]

a₁, b₁: Dimensions of figure 1 (m)
a₂, b₂: Dimensions of figure 2 (m)

Figure 2 Dimension b₂:

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1. What is a Similar Figures Proportion Calculator?

Definition: This calculator determines the missing dimension in similar geometric figures using the proportion between corresponding sides.

Purpose: It helps architects, designers, and students solve problems involving scaled drawings, model making, and geometric similarity.

2. How Does the Calculator Work?

The calculator uses the proportion formula:

\[ \frac{a_1}{a_2} = \frac{b_1}{b_2} \]

Where:

\( a_1, b_1 \) — Dimensions of figure 1 (m)
\( a_2, b_2 \) — Dimensions of figure 2 (m)

Explanation: The calculator solves for the missing dimension (b₂) by cross-multiplying the known values.

3. Importance of Proportion Calculation

Details: Maintaining proper proportions is essential when scaling designs, creating models, or working with similar geometric shapes in construction and manufacturing.

4. Using the Calculator

Tips: Enter any three known dimensions (a₁, b₁, a₂) to calculate the fourth (b₂). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What are similar figures?
A: Similar figures have the same shape but different sizes, with all corresponding angles equal and sides proportional.

Q2: Can I use different units for dimensions?
A: Yes, but all dimensions must use the same unit (all meters or all inches, etc.).

Q3: What if I know b₂ but need to find a different dimension?
A: Rearrange the formula accordingly: a₁ = (a₂ × b₁)/b₂, etc.

Q4: Does this work for 3D objects?
A: Yes, the same proportion applies to all corresponding linear dimensions of similar 3D objects.

Q5: How precise should my measurements be?
A: Use measurements with the same precision as your most precise known dimension for accurate results.