  The experimental observation of a spin-gap in the antiferromagnetic spin-1/2
compound $CaV_4O_9$ has been attributed to the formation of a plaquette
resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square
lattice. We construct a spin-1/2 model on the 1/5-depleted lattice for which
the PRVB state can be shown to be the exact ground state in a particular
parameter regime. In a subspace of this parameter regime, the first excited
state can be calculated exactly. In a different parameter regime, the dimer
state is shown to be the exact ground state.
