16. As shown in the figure, in trapezoid $\mathrm{ABCD}$, $\mathrm{AD}$ is parallel to $\mathrm{BC}$, and $\mathrm{BC}: \mathrm{AD}=5: 7$. Point $\mathrm{F}$ is on segment $\mathrm{AD}$, and point $\mathrm{E}$ is on segment $\mathrm{CD}$, satisfying $\mathrm{AF}: \mathrm{FD}=4: 3, \mathrm{CE}: \mathrm{ED}=2: 3$. If the area of quadrilateral $\mathrm{ABEF}$ is 123, then the area of $\mathrm{ABCD}$ is?
【Answer】 180
Analysis: (To simplify the calculation, we can assume it is a right trapezoid. Of course, when it is not a right trapezoid, a perpendicular line can be drawn from point E, at which time the heights of DEF and BCE are still 3:2, set as 3y and 2y, respectively, and the subsequent steps remain unchanged.)
Let AD=7x, BC=5x, DC=5y. Then DF=3x, DE=3y, EC=2y.
The area of trapezoid S = (AD + BC) × CD ÷ 2 = 30xy,
and the area of S_ABEF = S_ABCD - S_DEF - S_BEC = 30xy - 9/2xy - 5xy = 41/2xy = 123, so xy = 6, and the required area is 180.