3. Given quadrilateral $A B C D$ is an isosceles trapezoid, $A B / / C D, A B=6, C D=16 . \triangle A C E$ is a right triangle, $\angle A E C=90^{\circ}, C E=B C=A D$. Then the length of $A E$ is . $\qquad$
3. $4 \sqrt{6}$.

As shown in Figure 2, draw $A F \perp C D$ at point $F$. Then
$$
D F=5, C F=11 \text {. }
$$

Let $C E=B C$
$$
=A D=x \text {. }
$$

Thus, $A C^{2}=x^{2}+A E^{2}$, $A C^{2}=A F^{2}+11^{2}=x^{2}-5^{2}+11^{2}$.
Therefore, $x^{2}+A E^{2}=x^{2}-5^{2}+11^{2}$
$$
\Rightarrow A E^{2}=96 \Rightarrow A E=4 \sqrt{6} .
$$