Assuming the picture is a bit off (seems like a safe assumption given that the areas don't quite match), I'm going to assume that the rectangles are scaled in
Some nice integer side lengths that achieve these proportions are
These particular shapes allow for this interesting dissection:
All the horizontal bits are supposed to be of the same length (5 ...
A few possibilities, some of which are cheaty.
The simplest possibility, which I don't see anything in the story to rule out, is that
This still leaves unexplained
but there would seem to be many possibilities for that. This seems too straightforward an answer to be the intended solution, if this is a puzzle, but "in the real world" it would ...
I think the answer might be
My prefix is not known,
Rather it has some meaning or some mark,
But my suffix has magic powers,
And my infix depends on smart remark.
My whole is about choice, has a meaning or two.