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In the given trapezoid, we need to find the length of side \( AB \). We have the following information:

- \( ED = 9 \) cm (top parallel side),
- \( FC = 13 \) cm (middle parallel segment),
- \( DC = 4 \) cm, and
- \( AB \) is the base we need to determine.

The trapezoid has two non-parallel sides, \( AF \) and \( BE \), of 6 cm each, which implies this is an isosceles trapezoid. 

To find \( AB \), we can use the property that in an isosceles trapezoid, the average of the two parallel sides equals the length of the middle segment:
\[
\frac{ED + AB}{2} = FC
\]
Substituting the known values:
\[
\frac{9 + AB}{2} = 13
\]
Multiplying both sides by 2:
\[
9 + AB = 26
\]
Solving for \( AB \):
\[
AB = 26 - 9 = 17 \text{ cm}
\]

Thus, the correct answer is:
**C. 18 cm**

Do you want further details or have any questions?

Here are five related questions for deeper exploration:
1. How can we verify the isosceles property in trapezoids?
2. What are other methods to calculate unknown lengths in trapezoids?
3. How does the mid-segment theorem apply in other quadrilaterals?
4. How would this change if the trapezoid were not isosceles?
5. What are the properties of trapezoids in coordinate geometry?

**Tip:** For trapezoids, remember that the mid-segment (if parallel to the bases) often provides a quick way to find unknown side lengths.

Learn how to find the length of the base AB in an isosceles trapezoid given the lengths of the top side, middle segment, and non-parallel sides. Understand the application of the midsegment theorem and key trapezoid properties.

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