1. **State the problem:** We have a trapezoid with one base of length 16 ft, height 8 ft, and two slant sides each with horizontal length $x$. The total area is 176 square feet. We need to find $x$. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two parallel bases, and $h$ is the height. 3. **Identify known values:** - One base $b_1 = 16$ ft - Height $h = 8$ ft - Area $= 176$ sq ft - The other base $b_2$ is unknown but can be expressed in terms of $x$. 4. **Express the unknown base $b_2$:** Since the trapezoid has two slant sides each with horizontal length $x$, the bottom base is the top base plus twice $x$: $$b_2 = 16 + 2x$$ 5. **Set up the area equation:** $$176 = \frac{(16 + (16 + 2x))}{2} \times 8$$ 6. **Simplify inside the parentheses:** $$176 = \frac{(32 + 2x)}{2} \times 8$$ 7. **Simplify the fraction:** $$176 = (\cancel{\frac{32 + 2x}{2}}) \times 8$$ $$176 = (16 + x) \times 8$$ 8. **Divide both sides by 8:** $$\frac{176}{8} = 16 + x$$ $$22 = 16 + x$$ 9. **Solve for $x$:** $$x = 22 - 16$$ $$x = 6$$ **Final answer:** $$\boxed{6}$$ ft