Taxicab/Tenney version of heron's formula?

In order to quantify straightness, I tried to come up with a formula
that would give the 'area' of a bivector regardless of which basis
vectors are chosen to define it. For example, 12-tone periodicity
blocks obviously all have the same 'area' regardless of whether
they're defined using {81:80, 125:128}, {81:80, 648:625}, or what
have you. But when dealing with, say, 7-limit linear temperaments,
you can't simply quantify the area of the vanishing bivector using a
number of notes. I tried heron's formula using the Tenney lengths of
various equivalent dependent triples to determine the area (really
half the area) of the bivector, and it's almost independent of which
triple I use, but not quite. Any suggestions?