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To find the scale factor that takes trapezoid \( E \) to trapezoid \( F \), we can compare corresponding side lengths of the two trapezoids.

The side lengths of trapezoid \( E \) are:
- Top side: 15 units
- Bottom side: 20 units
- Left and right sides: 15 units

The side lengths of trapezoid \( F \) are:
- Top side: 18 units
- Bottom side: 24 units
- Left and right sides: 18 units

The scale factor is the ratio of the corresponding side lengths of trapezoid \( F \) to trapezoid \( E \). Let's calculate it:

\[
\text{Scale Factor} = \frac{\text{Corresponding side of } F}{\text{Corresponding side of } E}
\]

Using the top side lengths:

\[
\text{Scale Factor} = \frac{18}{15} = \frac{6 \times 3}{5 \times 3} = \frac{6}{5} = 1.2
\]

This ratio should be the same for all corresponding sides:

Using the bottom side lengths:

\[
\text{Scale Factor} = \frac{24}{20} = \frac{6 \times 4}{5 \times 4} = \frac{6}{5} = 1.2
\]

Therefore, the scale factor that takes trapezoid \( E \) to trapezoid \( F \) is **1.2**.

Would you like more details or have any questions? Here are some related questions you might find useful:

1. How do we calculate the area of trapezoid \( F \) using the scale factor?
2. What is the relationship between the scale factor and the perimeters of the trapezoids?
3. If the height of trapezoid \( E \) is known, how does the height of trapezoid \( F \) relate to it?
4. What happens to the angles of a trapezoid when it is scaled?
5. Can the scale factor be used to find the ratio of the areas of the two trapezoids?

**Tip:** When dealing with similar figures, the ratio of their areas is the square of the scale factor.

What scale factor takes trapezoid E to trapezoid F?

Learn how to calculate the scale factor that transforms trapezoid E into trapezoid F by comparing corresponding sides. The problem involves geometric concepts such as ratios and scaling, suitable for students in Grades 6-8.

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