Three of the four sides of a certain quadrilateral have lengths of 3, 4, and 5, and two of its four angles measure 90°. Let *A* be the sum of all possible *distinct* areas this quadrilateral could have. What is \(\lfloor A \rfloor\)?

**Details and assumptions**

- If more than one such quadrilateral has the same area, only count that area once.
- The fourth side can have any positive length, and the other two angles can have any measure.
- If the fourth side has length 0, then that is not a quadrilateral.

*Photo credit: http://ds9.trekcore.com/gallery/albums/publicityphotos/odo/odo4.jpg*

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