6. (3 points) The upper base of the trapezoid is 5, the lower base is 10, and the two legs are 3 and 4, respectively. What is the area of the trapezoid?
【Solution】Solution: As shown in the figure, draw $A E / / B C$ intersecting $D C$ at $E$, and draw $A F \perp D C$ at $F$. Then, quadrilateral $A B C E$ is a parallelogram, $A E=B C=4, D E=10-5=5$, and it is known that $A D=3$. According to the Pythagorean theorem, $\triangle A D E$ is a right triangle,
$$
A F=3 \times 4 \div 5=2.4, S_{\text {trapezoid } A B C E}=(5+10) \times 2.4 \div 2=18 \text {; }
$$

Therefore, the answer is: 18.