Suppose we break a stick of length one at four randomly and independently chosen points and that the resulting pieces form a pentagon.

Such a pentagon can be formed with probability $1-(5/16) = {11\over16}$ (see https://atlas.mat.ub.edu/personals/dandrea/emiliano_gomez.ps, which states that an $n$-gon is formed from $n-1$ breaks with probability $1-{n\over2^{n-1}}$).

Using this distribution of lengths and assuming that a cyclic pentagon has been formed, what is the expected value of the pentagon's area?