  We calculate and measure the density distribution and cloud size of a trapped
two-dimensional $^{6}$Li Fermi gas near a Feshbach resonance at low
temperatures. Density distributions and cloud sizes are calculated for a wide
range of interaction parameters using a local density approximation (LDA) and a
zero-temperature equation of state obtained from quantum Monte Carlo
simulations reported by G. Bertaina and S. Giorgini, Phys. Rev. Lett.
\textbf{106}, 110403 (2011). We find that LDA predictions agree well with
experimental measurements across a Feshbach resonance. Theoretical results for
Tan's contact parameter in a trapped gas are reported along with predictions
for static structure factor at large momentum which could be measured in future
Bragg spectroscopy experiments on two-dimensional Fermi gases.
