Establish a spatial rectangular coordinate system D-xyz with D as the origin, DC as the X axis, DA as the Y axis and DD 1 as the Z axis.

Point coordinates:

D(0，0，0)、A(0， 1，0)、B( 1， 1，0)、C( 1，0，0)、D 1(0，0， 1)、A 1(0， 1， 1)、B 1( 1)、B 1( 1，

P( 1， 1/2，0)，Q( 1，0，z)

The vector PA=(- 1,1/2,0) and the vector pq = (0 0,01/2,z).

Let m (0,0, m) be a point on the Z axis, and the normal vector of the surface APQM is n.

∴n= vector PA× vector PQ=(z/2, z, 1/2)

Vector AM=(0,-1, m)

Let the vector am n = 0-z+m/2 = 0 = > m = 2z.

∴M(0,0,2z),CQ=z,DM=2z

① When 0

② when CQ= 1/2, m and D 1 coincide, PQ//AM, QM=AP=√5/2, and s is an isosceles trapezoid, which is correct;

③ When CQ=3/4, DM=3/2, S intersects with C 1D 1 in R, Q intersects with QE //CD intersects with E in DM, ⊿ MD 1R ⊿ MEQ.

∴MD 1/ME=D 1R/EQ

MD 1 = 3/2- 1 = 1/2，ME=3/2-3/4=3/4

∴md 1/me=d 1r/eq=2/3==>； D 1R=2/3== >c 1R = 1-2/3 = 1/3

correct

(4) when 3/4

wrong

⑤ When CQ= 1, s is APC 1F, which is a rhombus with a side length of √5/2, AC 1=√3 and PF=√2.

∴ Area = 1/2*√3*√2=√6/2

Correct.