1. **State the problem:** We have a parallelogram-based prism with volume 1430. The prism's base is a parallelogram with base length $b$ and height 11. The prism's length (height of the prism) is 10. We need to find the base $b$. 2. **Formula for volume of a prism:** $$\text{Volume} = \text{Base Area} \times \text{Length}$$ For a parallelogram base, the area is: $$\text{Base Area} = b \times h$$ where $b$ is the base length and $h$ is the height of the parallelogram. 3. **Apply the formula:** Given: $$\text{Volume} = 1430, \quad h = 11, \quad \text{Length} = 10$$ So, $$1430 = (b \times 11) \times 10$$ 4. **Simplify the equation:** $$1430 = 110b$$ 5. **Solve for $b$:** Divide both sides by 110: $$b = \frac{1430}{110}$$ Show cancellation: $$b = \frac{\cancel{110}13}{\cancel{110}1} = 13$$ 6. **Final answer:** $$\boxed{13}$$ The base length $b$ of the parallelogram is 13.