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

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 $k$, then the ratio of the areas will be $k^2$.

3. ### Analysis and Detail

Assuming the scale factor of the sides is $k$:

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

4. ### Verify and Summarize

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

• The ratio of their areas is $k^2$.

Final Answer

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