To find the scale factor that takes trapezoid F to trapezoid G, we compare the corresponding sides of the two trapezoids. Since trapezoid G is a scaled copy of trapezoid F, the scale factor should be consistent across all corresponding sides.

Given:

• Top side of trapezoid F = 25
• Bottom side of trapezoid F = 12
• Top side of trapezoid G = 32.5
• Bottom side of trapezoid G = 15.6
• Side of trapezoid G = 37.7 (assuming this is a non-parallel side)

Let's calculate the scale factor for the top and bottom sides:

For the top sides: $\text{Scale factor (top)} = \frac{\text{Top side of G}}{\text{Top side of F}} = \frac{32.5}{25} = 1.3$

For the bottom sides: $\text{Scale factor (bottom)} = \frac{\text{Bottom side of G}}{\text{Bottom side of F}} = \frac{15.6}{12} = 1.3$

Both the top and bottom sides yield a scale factor of 1.3.

Thus, the scale factor that takes trapezoid F to trapezoid G is 1.3.

Would you like more details or have any questions?

Here are some related questions:

1. How do non-parallel sides of trapezoids scale when the trapezoid is scaled?
2. What happens to the angles of a trapezoid when it is scaled?
3. How can you find the area of trapezoid G given the scale factor and the area of trapezoid F?
4. What other properties of trapezoids remain unchanged under scaling?
5. How does the scale factor affect the perimeter of trapezoid G compared to trapezoid F?

Tip: When working with scale factors, ensure to compare corresponding sides accurately, and remember that the scale factor applies consistently to all sides of the figure.