  A moderately spinning neutron star acquires an oblate shape and a spacetime
with a significant quadrupole moment. These two properties affect its apparent
surface area for an observer at infinity, as well as the lightcurve arising
from a hot spot on its surface. In this paper, we develop a ray-tracing
algorithm to calculate the apparent surface areas of moderately spinning
neutron stars making use of the Hartle-Thorne metric. This analytic metric
allows us to calculate various observables of the neutron star in a way that
depends only on its macroscopic properties and not on the details of its
equation of state. We use this algorithm to calculate the changes in the
apparent surface area, which could play a role in measurements of neutron star
radii and, therefore, in constraining their equation of state. We show that
whether the spinning neutron star appears larger or smaller than its
non-rotating counterpart depends primarily on its equatorial radius. For
neutron stars with radii ~10 km, the corrections to the Schwarzschild spacetime
cause the apparent surface area to increase with spin frequency. In contrast,
for neutron stars with radii ~15 km, the oblateness of the star dominates the
spacetime corrections and causes the apparent surface area to decrease with
increasing spin frequency. In all cases, the change in the apparent geometric
surface area for the range of observed spin frequencies is < 5% and hence only
a small source of error in the measurement of neutron star radii.
