1. **State the problem:** We are given a trapezoid BADC with bases BC = 12 cm and AD = 26 cm. We need to find the length of the median EF, where EF is parallel to the bases and connects points E on AB and F on DC. 2. **Formula for the median of a trapezoid:** The median (also called the mid-segment) of a trapezoid is the segment that connects the midpoints of the non-parallel sides. Its length is the average of the lengths of the two bases. $$EF = \frac{BC + AD}{2}$$ 3. **Apply the formula:** Substitute the given base lengths: $$EF = \frac{12 + 26}{2}$$ 4. **Simplify the expression:** $$EF = \frac{38}{2}$$ 5. **Calculate the final answer:** $$EF = 19$$ 6. **Interpretation:** The length of the median EF is 19 cm. **Final answer:** 19 cm