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.