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.