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The problem provides that the length scale factor from pentagon \( B \) to pentagon \( A \) is \( \frac{1}{3} \). Now, we need to find the **area scale factor** from pentagon \( B \) to pentagon \( A \).

The area scale factor is the square of the length scale factor. So, if the length scale factor is \( \frac{1}{3} \), the area scale factor is:

\[
\left( \frac{1}{3} \right)^2 = \frac{1}{9}
\]

Thus, the area scale factor from pentagon \( B \) to pentagon \( A \) is \( \frac{1}{9} \).

Do you have any questions or need further details?

Here are 5 related questions for further practice:
1. What would be the area scale factor if the length scale factor was \( \frac{2}{5} \)?
2. How do you calculate the volume scale factor if given a length scale factor?
3. If the area scale factor is \( \frac{1}{16} \), what is the corresponding length scale factor?
4. How do the perimeters of two similar figures relate to their length scale factor?
5. Can two figures have the same area but different length scale factors?

**Tip:** For similar shapes, the area scale factor is always the square of the length scale factor, and the volume scale factor is the cube of the length scale factor!

The length scale factor from pentagon B to pentagon A is 1/3. Find the area scale factor from pentagon B to pentagon A.

Learn how to find the area scale factor from pentagon B to pentagon A, given that the length scale factor is 1/3. This problem involves understanding the relationship between length and area in similar figures. Suitable for students in Grades 8-10.

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