Area laws were first discovered by Bekenstein
and Hawking, who found that the entropy of a
black hole grows proportional to its surface
area, and not its volume. Entropy area laws
have since become a fundamental part of modern
physics, from the holographic principle in
quantum gravity to ground state wavefunctions of
quantum matter, where entanglement entropy is
generically found to obey area law scaling. As
no experiments are currently capable of directly
probing the entanglement area law in naturally
occurring many-body systems, evidence of its
existence is based on studies of simplified
theories. Using new exact microscopic path
integral ground state Monte Carlo simulations of
superfluid 4He, we demonstrate for the first
time area law scaling of entanglement entropy in
a real quantum liquid in three dimensions. We
validate the fundamental principles underlying
its physical origin, and present an
"entanglement equation of state" showing how it
depends on the density of the superfluid.