1. **State the problem:** We have two similar trapezoidal shapes A and B. Shape A has sides: top = 5 cm, bottom = 7 cm, height = 15 cm. Shape B has sides: top = 4 cm, height = 12 cm, bottom = t cm. We need to find: - The scale factor from shape A to shape B. - The value of t. 2. **Formula and rules:** For similar shapes, corresponding sides are proportional. The scale factor $k$ from shape A to shape B is given by: $$k = \frac{\text{side in B}}{\text{corresponding side in A}}$$ All corresponding sides have the same scale factor. 3. **Calculate the scale factor using the top sides:** $$k = \frac{4}{5}$$ 4. **Verify scale factor with heights:** $$k = \frac{12}{15} = \frac{\cancel{3} \times 4}{\cancel{3} \times 5} = \frac{4}{5}$$ This confirms the scale factor is $\frac{4}{5}$. 5. **Find $t$ using the bottom sides:** Since the scale factor is $\frac{4}{5}$, we have: $$\frac{t}{7} = \frac{4}{5}$$ Multiply both sides by 7: $$t = 7 \times \frac{4}{5} = \frac{28}{5}$$ 6. **Final answers:** - Scale factor from shape A to shape B is $\frac{4}{5}$. - Value of $t$ is $\frac{28}{5}$. These fractions are already in simplest form.