  We report on the measurement of the equation of state of a two-component
Fermi gas of $^6$Li atoms with resonant interactions. By analyzing the
\textit{in situ} density distributions of a population-imbalanced Fermi mixture
reported in the recent experiment [Y. Shin \textit{et al.}, Nature
\textbf{451}, 689 (2008)], we determine the energy density of a resonantly
interacting Fermi gas as a function of the densities of the two components. We
present a method to determine the equation of state directly from the shape of
the trapped cloud, where the fully-polarized, non-interacting ideal Fermi gas
in the outer region provides the absolute calibration of particle density. From
the density profiles obtained at the lowest temperature, we estimate the
zero-temperature equation of state.
