A) Admirable solution, nicely presented.
B) Working backwards is a good problem solving strategy, but make sure to present solutions arguing forward from known information and facts.
C) Complete solution, or close enough; fine job.
D) The proof was difficult to decipher because of a confusing or illegible presentation.
E) The paper did not merit any points, but the response was quite enjoyable to read!
G) You found the correct theoretical minimum using Brahmagupta's formula; now just explain how we now it is possible to achieve this small an area.
H) Half the question was answered correctly; the other half was omitted or no headway was made.
J) The triangle inequality does imply that y+z>4 and w+x>5, so the area is at least 20. But this bound is not sharp; in other words, there is no diagram that simultaneously gives y+z=4 and w+x=5.
K) Good job, but be sure to justify why (or how) you are counting the triangle twice.
L) Fine answer, but more work than necessary; it is OK to be more concise or cite previous results.
M) Mostly there; main ideas are correct but points deducted for missing details or too brief a proof.

N) Not bad; careless mistakes or a false statement tarnish an otherwise correct solution.
O) Omitted problem or no attempt at a proof.
P) Note that point P can be located outside of the rectangle, which allows for the possibility of even smaller areas.
Q) Your response contained good ideas which did not lead (unfortunately) to a solution.
R) On the right track or a few of the correct ideas present, so deserving of some credit.
T) One can achieve the theoretical minimum of 24. To do this, you'll need a quadrilateral whose opposite angles sum to 0. This is actually possible, with a self-intersecting cyclic quadrilateral using signed angles. (See the diagram in the solution.)
W) On the wrong track or a very difficult approach, but warranting some credit.
Y) Little or no significant progress towards a solution (occasionally despite a fair amount of work), or misinterpretion of the question.
Z) The solution was sufficient to warrant full credit, but it would still be a good idea to provide more justification or supporting details.