Good question, eta. Atomica (AHD 2000) give this:
[Late Latin trapezium, trapezoid, from Greek trapezion, diminutive of trapeza, table : tra-, four + peza, foot.] That got me thinking: four feet, four feet...because you have to use all four "feet" to get up TO the high wire? Because you have to use all four to keep your balance once you're on it? Dr. Bill's surmise may be the correct one; I truly can't guess.