Because $\overline{AB} \parallel \overline{CD}$, angles formed with the diagonal $\overline{BD}$ can be matched as equal angles.

Once you identify similar triangles, relate the segments on diagonal $AC$ (the pieces $AE$ and $EC$) to the parallel bases $AB$ and $CD$.

Use the proportion $\frac{7.2}{x}=\frac{8}{18}$. In Desmos, graph:

• $y=7.2/x$
• $y=8/18$

Click the intersection point of the two graphs. The $x$-coordinate is the value that makes the proportion true.

The $x$-coordinate from the intersection represents the length of $\overline{EC}$.

Consider $\triangle ABE$ and $\triangle CDE$.

• $\angle AEB$ and $\angle CED$ are vertical angles, so they are equal.
• $\angle ABE$ equals $\angle CDE$ because $\overline{AB} \parallel \overline{CD}$ and $\overline{BD}$ is a transversal.

Therefore, $\triangle ABE \sim \triangle CDE$.

From the similarity, corresponding sides are proportional:

Substitute the given values:

Cross-multiply:

So

Therefore, the length of $\overline{EC}$ is 16.2.