The maximum area is 6. I made it myself. I don't know if it's right. The idea is this: in order to maximize the area, the upper and lower floors have been set, so the height should be as large as possible. Maximize the height, then △BCD should be an isosceles right triangle. Because BC = 4, what about BD? +CD？ =4? = 16, what about BD? = 16 \2 = 8, BD=√8=2√2. If D is the vertical line of BC and the vertical foot is E, then we get1/2× BD× CD =1/2× BC× DE by equal product, that is, BD× CD =

It's detailed enough. . . I type one word at a time. I hope it's not garbled. . . Must adopt!