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In this paper, we study the minimizing property for the isosceles trapezoid solutions of the four-body problem. We prove that the minimizers of the action functional restricted to homographic solutions are the Keplerian elliptical solutions, and this functional has a minimum equal to 32 (2) ^2/3T^1/3 ( (a, b) (a, b) ) ^2/3. Further, we investigate the dynamical behavior in the trapezoidal four-body problem using the Poincaré surface of section method.
Mansur et al. (Sun,) studied this question.