  The Gaia data give us an unprecedented view to the 3-dimensional (3D)
structure of molecular clouds in the Solar neighbourhood. We study how the
projected areas and masses of clouds, and consequently the Kennicutt-Schmidt
relation (KS-relation), depend on the viewing angle. We derive the probability
distributions of the projected areas and masses for nine clouds within 400 pc
from the Sun using 3D dust distribution data from the literature. We find that
the viewing angle can have a dramatic effect on the observed areas and masses
of individual clouds. The joint probability distributions of the areas and
masses are strongly correlated, relatively flat, and can show multiple peaks.
The typical ranges and 50% quartiles of the distributions are roughly 100-200%
and 20-80% of the median value, respectively, making viewing angle effects
important for all individual clouds. The threshold value used to define the
cloud areas is also important; our analysis suggests that the clouds become
more anisotropic for smaller thresholds (larger scales). On average, the areas
and masses of the plane-of-the-sky and face-on projections agree, albeit with a
large scatter. This suggests that sample averages of areas and masses are
relatively free of viewing angle effects, which is important to facilitate
comparisons of extragalactic and galactic data. Ultimately, our results
demonstrate that a cloud's location in the KS-relation is affected by viewing
angle in a non-trivial manner. However, the KS-relation of our sample as a
whole is not strongly affected by these effects, because the co-variance of the
areas and masses causes the observed mean column density to remain relatively
constant.
