 If the scale factor of the sides of two similar polygons is m/n then what is the ratio of the areas?

When two polygons are similar, the ratio of their areas is the square of the ratio of their corresponding side lengths. 

If the scale factor of the sides of two similar polygons is \( \frac{m}{n} \), then the ratio of their areas is given by:

\[
\left(\frac{m}{n}\right)^2 = \frac{m^2}{n^2}
\]

### Example:

- If \( m = 2 \) and \( n = 3 \), the ratio of their areas would be:
  \[
  \left(\frac{2}{3}\right)^2 = \frac{4}{9}
  \]

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you find the scale factor of two similar polygons?
2. What is the ratio of volumes for similar 3D shapes given their scale factor?
3. How do you determine if two polygons are similar?
4. How does the perimeter ratio of similar polygons compare to their side length ratio?
5. Can the concept of similar polygons be applied to non-polygonal shapes like circles?

**Tip:** The ratio of areas is always the square of the ratio of corresponding sides for similar figures, regardless of the type of polygon.

Understand how to find the ratio of areas for similar polygons when given the scale factor of their sides. Example provided with detailed steps and calculations. Ideal for Grades 7-9 students learning about geometric similarity and area ratios.

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