1. **Stating the problem:** We need to find the length of segment $AB$ in a trapezoid where $DC = 11.5$ units, and $MN = 18.7$ units, with $MN$ parallel to both $AB$ and $DC$. 2. **Understanding the trapezoid and segments:** In trapezoids, segments parallel to the bases and between them often relate by the properties of similar triangles or mid-segment theorems. 3. **Using the trapezoid mid-segment theorem:** The segment $MN$ is parallel to both bases $AB$ and $DC$. If $MN$ is the mid-segment between $AB$ and $DC$, then its length is the average of the lengths of $AB$ and $DC$: $$MN = \frac{AB + DC}{2}$$ 4. **Substitute known values:** $$18.7 = \frac{AB + 11.5}{2}$$ 5. **Solve for $AB$:** Multiply both sides by 2: $$2 \times 18.7 = AB + 11.5$$ $$37.4 = AB + 11.5$$ Subtract 11.5 from both sides: $$37.4 - 11.5 = AB$$ $$\cancel{37.4} - \cancel{11.5} = AB$$ $$25.9 = AB$$ 6. **Final answer:** $$\boxed{AB = 25.9}$$ units.