It was proposed that target space entanglement is related to notions of entanglement in the bulk. To explore such a connection, we begin with 1/2 BPS states of N = 4 Yang Mills theory that are known to represent giant gravitons and their duals in supergravity. Noticed the connection of 1/2 BPS sector of N = 4 Yang-Mills theory on 3-sphere and the lowest Landau level (LLL), we consider the entanglement entropy of an arbitrary subregion in a system of N non-relativistic fermions in 2+1 dimensions in LLL states. By introducing an auxiliary 1+1 dimensional fermionic system, we derive an expression for the leading large-N contribution in terms of the expectation value of the phase space density operator in 1+1 dimensions. For the subregion much larger than the basic length scale of the theory, the latter can replaced by its semiclassical Thomas-Fermi value, yielding expressions in terms of explicit integrals which can be evaluated analytically. We show that the leading term in the entanglement entropy is a perimeter law with a shape-independent coefficient. Furthermore, we obtain analytic expressions for additional contributions from sharp corners on the entangling curve, which is purely geometric. In the 1/2 BPS side, we interpret the entanglement we consider as an entanglement in target space. Our future direction (on-going) is to uncover the meaning of this quantity in the full N = 4 SYM theory and its gravitational bulk.