||A new realisation of extended quantum-mechanical supersymmetry (QM SUSY) with central extension is investigated. We first show that two different sets of d + 2 (d + 1) supercharges for d = even (odd), each of which satisfies an N = d + 2 (d + 1) extended QM SUSY algebra without central extension, are hidden in the four-dimensional mass spectrum of the (4 + d)-dimensional Dirac action. We then find that the whole set of the supercharges forms an N = 2d + 4 (2d + 2) extended QM SUSY algebra with central charges for d = even (odd). The representation of the supersymmetry algebra is shown to be 1/2-Bogomol'nyi-Prasad-Sommerfield states that correspond to a short representation for the supersymmetry algebra with a central extension. We explicitly examine the four-dimensional mass spectrum of the models with the hyperrectangle and the torus extra dimensions, and discuss their supersymmetric structures.