To find the slant height of the pyramid, we can use the Pythagorean theorem. In the right triangle formed by the height of the pyramid, the distance from the center of the base to the midpoint of one side of the base, and the slant height, we have the following dimensions:
- The height of the pyramid (vertical side) = 12 units
- The distance from the center of the base to the midpoint of a side (horizontal side) = 4 units
Let \( s \) be the slant height. According to the Pythagorean theorem:
\[ s^2 = \text{(height)}^2 + \text{(half base distance)}^2 \]
Substituting the values:
\[ s^2 = 12^2 + 4^2 \] \[ s^2 = 144 + 16 \] \[ s^2 = 160 \] \[ s = \sqrt{160} \approx 12.649 \]
Rounding to the nearest tenth, the slant height \( s \) is approximately:
\[ \boxed{12.7} \]