For each possible triangulation, compute the smallest area triangle in it.
Print the largest smallest area triangle.

If that does not make much sense, let's go over the sample input:
The given quadrilateral can be triangulated in only two different ways. The areas of the resulting triangles are:

Cut #1: 11.5 + 16.0  (min. area triangle = 11.5)
Cut #2: 10.0 + 17.5  (min. area triangle = 10.0)
answer = max(11.5, 10.0) = 11.5

Good luck!