  We obtained a density-dependent analytical expression of binding energy per
nucleon for different neutron-proton asymmetry of the nuclear matter (NM) with
a polynomial fitting, which manifests the results of effective field theory
motivated relativistic mean-field (E-RMF) model. This expression has the edge
over the Br$\ddot{u}$ckner energy density functional [Phys. Rev. {\bf 171},
1188 (1968)] since it resolves the Coster-Band problem. The NM parameters like
incompressibility, neutron pressure, symmetry energy, and its derivatives are
calculated using the acquired expression of energy per nucleon. Further, the
weight function calculated by E-RMF densities are folded with calculated NM
parameters within coherent density fluctuation model to find the properties of
closed/semi-closed-shell even-even $^{16}$O, $^{40}$Ca, $^{48}$Ca, $^{56}$Ni,
$^{90}$Zr, $^{116}$Sn, and $^{208}$Pb nuclei. The values obtained for the
neutron pressure $P^{A}$, symmetry energy $S^{A}$ and its derivative
$L_{sym}^A$ known as slope parameter, lie within a narrow domain whereas there
is a large variation in isoscalar incompressibility $K^{A}$ and surface
incompressibility $K_{sym}^{A}$ while moving from light to heavy nuclei. The
sizable variation in $K^{A}$ and $K_{sym}^{A}$ for light and heavy nuclei
depicts their structural dependence due to the peculiar density distribution of
each nucleus. A comparison of surface quantities calculated in the present work
has also been made with ones obtained via Br$\ddot{u}$ckner energy density
functional.
