  In this article, we demonstrated a stellar model for compact star in presence
of strange matter embedded in $D\ge4$ dimensional space-time defind by
Finch-Skea metric. To study the relevant physical properties of the interior
matter, we consider the equation of state $(henceforth~EOS)$ as proposed in MIT
bag model given by $p=\frac{1}{3}(\rho-4B)$, where $B$ is termed as bag
constant. The Mass-Radius relationships in four and higher dimensions are
determined using the range of values of surface density through the relation
$\rho_{s}=4B$ for which bulk strange matter may be a viable issue for compact
objects. Here we choose the range of $B$ such that stable strange matter may
exist at zero external pressure relative to neutron. We note that a maximum
value of the stellar radius is exist when $B$ is fixed at a given allowed value
for which metric functions considered here to be real. This is the maximum
allowed radius $(b_{max})$ in this model which depends on surface density of a
strange star. In four dimensions the compactness of a star is found to be
greater than 0.33. In case of higher dimensions ($D>4$), we observed different
values of compactness. Causality conditions are satisfied interior to the star
upto maximum allowed radius $(b_{max})$ for which metric function is real. The
validity of energy conditions, surface red-shift and other parameters of the
stellar configuration are studied and found new results. Stability of the
system is also studied.
