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