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I would know how to calculate C of the funny capacitor, at
least in principle, if the potential of the bottom plate were
specified,
for example zero.
In that case I would impose
potentials on vertical plates, for example, -50 and +50 V,
and used the Laplace equation to find surface charges
on each vertical plate. Then C=Q/V.
The boundary
conditions (potentials on three objects) is given and the
rest is just a matter of number crunching.
floating.