Using a quaternionic formulation of the moduli space M(IIA/K3) of 10D type IIA superstring on a generic K3 complex surface with volume V, we study extremal N=2 black attractors in 6D space-time and their uplifting to 7D. For the 6D theory, we exhibit the role played by 6D N=1 hypermultiplets and the Z central charges isotriplet of the 6D N=2 superalgebra. We construct explicitly the special hyper-Kähler geometry of M(IIA/K3) and show that the SO(4)×SO(20) invariant hyper-Kähler potential is given by H=H+Tr[ln(1-V0-1S)] with Kähler leading term H=Tr[lnV] plus an extra term which can be expanded as a power series in V0-1 and the traceless and symmetric 3×3 matrix S. We also derive the holomorphic matrix prepotential G and the flux potential G of the 6D black objects induced by the topology of the RR field strengths F=dA and F=dA on the K3 surface and show that G reads as Q+∑m=13qZ. Moreover, we reveal that Z=∑I=120Q(∫J) where the isotriplet J is the hyper-Kähler 2-form on the K3 surface. It is found as well that the uplifting to seven dimensions is quite similar to 4D/5D correspondence for back hole potential considered in arXiv: 0707.0964 [hep-ph]. Then we study the N=2 black object attractors in 6D and 7D obtained respectively from type IIA string and M-theory on K3.