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If the scale factor of the sides of two similar polygons is   then the ratio of the areas is Blank 1 Question 14 .

Question

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Solution

To determine the ratio of the areas of two similar polygons given the scale factor, we must utilize the properties of similar figures.

1. ### Break Down the Problem

The problem requires us to find out how the ratio of the sides of two similar polygons relates to the ratio of their areas.

2. ### Relevant Concepts

When dealing with similar figures:

  • If the ratio of the lengths of the corresponding sides (scale factor) is k k , then the ratio of the areas will be k2 k^2 .

3. ### Analysis and Detail

Assuming the scale factor of the sides is k k :

  • The areas will be related by Area ratio=k2 \text{Area ratio} = k^2 .

4. ### Verify and Summarize

To summarize, if the polygons are similar and the scale factor of their corresponding sides is k k , then:

  • The ratio of their areas is k2 k^2 .

Final Answer

If the scale factor of the sides of two similar polygons is k k , then the ratio of the areas is k2 k^2 .

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