What length base y must the triangle in the diagram have, if the volume of the triangular prism has to be 800 cm³ ? Round off to one decimal place.

The volume $V$ of a triangular prism is given by the formula:

$$V = \frac{1}{2} \times \text{base of triangle} \times \text{height of triangle} \times \text{length of prism}$$

Using the variables from the diagram:

$$V = \frac{1}{2} \times y \times 12 \text{ cm} \times 8 \text{ cm}$$

We are given that the volume $V = 800 \text{ cm}^3$.

$$800 \text{ cm}^3 = \frac{1}{2} \times y \times 12 \text{ cm} \times 8 \text{ cm}$$

First, multiply the known numerical values:

$$800 = \frac{1}{2} \times y \times (12 \times 8)$$ $$800 = \frac{1}{2} \times y \times 96$$

Now, multiply $\frac{1}{2}$ by 96:

$$800 = 48y$$

To find $y$, divide both sides by 48:

$$y = \frac{800}{48}$$ $$y = 16.666... \text{ cm}$$

Rounding 16.666... to one decimal place gives 16.7.

$$y \approx 16.7 \text{ cm}$$

The length base $y$ must be $\boxed{\text{16.7 cm}}$.