1. **State the problem:** We have two similar shapes A and B. Shape A has height 8.5 cm and base width 3 cm. Shape B has base width 12 cm and unknown height $h$. We need to find $h$ using similarity. 2. **Understand similarity:** Similar shapes have corresponding lengths in the same ratio. So, the ratio of heights equals the ratio of base widths. 3. **Set up the ratio:** $$\frac{h}{8.5} = \frac{12}{3}$$ 4. **Simplify the right side:** $$\frac{12}{3} = 4$$ 5. **Solve for $h$:** $$h = 8.5 \times 4 = 34$$ 6. **Answer:** The height $h$ of shape B is **34 cm**.