https://file.aiquickdraw.com/mathbot/file/17292129352707x22rpz1.jpg

The problem provided involves two similar trapezoids, \( ABCD \) and \( WXYZ \). The given measurements are:

- \( AB = 24 \) inches, \( AD = 18 \) inches for trapezoid \( ABCD \).
- \( WX = 6 \) inches, \( XY \) is unknown (labeled \( ZW \)) for trapezoid \( WXYZ \).

Since these shapes are similar, the corresponding sides are proportional. We can set up a proportion using corresponding sides from the two shapes.

The corresponding sides are:
- \( AB \) corresponds to \( WX \),
- \( AD \) corresponds to \( WZ \).

Let's set up the proportion using \( AB \) and \( WX \):
\[
\frac{AB}{WX} = \frac{AD}{ZW}
\]
Substitute the known values:
\[
\frac{24}{6} = \frac{18}{ZW}
\]
Simplify:
\[
4 = \frac{18}{ZW}
\]
Now solve for \( ZW \):
\[
ZW = \frac{18}{4} = 4.5 \, \text{inches}
\]

Thus, the length of side \( ZW \) is **4.5 inches**.

Would you like any further explanation? Here are some related questions for practice:

1. How do you identify corresponding sides in similar figures?
2. What are the properties of similar trapezoids?
3. How can you set up proportions for other sides of the trapezoids?
4. What happens if the scale factor between two shapes is not an integer?
5. How can you apply the concept of similar figures to triangles?

**Tip**: In similar figures, all corresponding angles are equal, and the lengths of corresponding sides are proportional.

In the image, shape ABCD is similar to shape WXYZ. Find the measure of side ZW.

This problem helps students understand how to find the length of a side in similar trapezoids using proportions. Given two similar shapes, ABCD and WXYZ, students solve for ZW using the corresponding sides AB and WX. Suitable for Grades 7-9, this problem reinforces the concept of proportional sides in similar figures.

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