There are three small questions in this question, and the answers are as follows: (1) DG⊥AB at G point and CH⊥AB at H point pass through D and C respectively. .........................................................................................................

∫AB‖CD，

∴ DG=CH，DG‖CH

∴ Quadrilateral DGHC is a rectangle, GH = CD = 1.

DG = CH，AD=BC，∠AGD=∠BHC=90，

∴△AGD?△bhc(HL)。

∴ Joint-stock company = BH = = 3......................2 points.

∵ at Rt△AGD, ag = 3, ad = 5,

∴ DG=4。

∴ .............................................. 3 points.

(2)mn‖ab,me⊥ab,nf⊥ab，

∴ ME=NF，ME‖NF。

∴ quadrilateral MEFN is a rectangle.

∫AB‖CD，AD=BC，

∴ ∠A=∠B

ME = NF，∠MEA=∠NFB=90，

∴△mea?△nfb(AAS)。

∴ AE = BF ................................. 4 points.

Let AE = X, then EF = 7-2x .......................... 5 points.

∠∠A =∠A，∠MEA=∠DGA=90，

∴ △MEA∽△DGA。

∴ .

I = ............................................... 6 points.

....................................., 8 points.

When x =, me = < 4, and the maximum MEFN area of ∴ quadrilateral is 9 points.

(3) ........................................................................................................................ 10.

From the formula (2), let AE = x, then EF = 7-2x, Me =.

If the quadrilateral MEFN is a square, then me = ef.

That is, if the solution is 7-2x, the score is .................................................. 1 1.

∴ EF=