Mental Puzzle! ^_^

First, please view this question: http://openstudy.com/study#/updates/500c014fe4b0549a892fe7dc

Now my question is this:
How many combinations of WHOLE # units are there for the dimensions that can yield that total area?

To be clear:
No fractions.
No roots.
No irrationals.
No imaginary #'s.
Just strictly whole # units, how many combinations are possible?

Have at it math people! I look forward to seeing your methods! (please don't just post your combination total, show us what you did to do it)

Question

Mental Puzzle!  ^_^

First, please view this question:  http://openstudy.com/study#/updates/500c014fe4b0549a892fe7dc

Now my question is this:
How many combinations of WHOLE # units are there for the dimensions that can yield that total area?

To be clear:
No fractions.  
No roots.  
No irrationals.  
No imaginary #'s.  
Just strictly whole # units, how many combinations are possible?

Have at it math people!   I look forward to seeing your methods!  (please don't just post your combination total, show us what you did to do it)

anonymous · Answer

For reference: an isosceles trapezoid with an area of 21540 ft$^2$ http://mathworld.wolfram.com/IsoscelesTrapezoid.html

anonymous · Answer

Make sense?  ^_^

anonymous · Answer

Related example done, to show visually what I mean
|dw:1342968040706:dw|

1m * 16m = 16m$^2$ is also valid, however...

2$\sqrt{2}$m * 4$\sqrt{2}$m = 16 m$^2$ gives the right area, sure; but is INVALID for this question, whole units only.  $\sqrt{2}$ isn't a whole number :-)