3. Given the side lengths of a trapezoid are $3,4,5,6$. Then the area of this trapezoid is $\qquad$ .
3. 18.

First, determine the lengths of the two bases. As shown in Figure 7, let trapezoid $ABCD$ have $AD$ and $BC$ as the upper and lower bases, respectively. Draw $AE \parallel CD$. Then $BE$ is the difference between the upper and lower bases.

In $\triangle ABE$, $AB - AE = AB - CD < BE = BC - AD$. Therefore, $AB = 5, CD = 4, AD = 3, BC = 6$. In $\triangle ABE$, $AB = 5, BE = 3, AE = CD = 4$. Thus, $AE$ is the height of the trapezoid.
Therefore, $S_{\text{trapezoid}} = \frac{1}{2} \times (3 + 6) \times 4 = 18$.