remember the requirements for aromaticity:
cyclic
planar
and Huckel's rue
annulene has 10 carbons, therefore, the strain on the ring forces the carbons pi orbitals to lie in different planes.
napthalene is basically 2 benzene rings which we known are definitely aromatic. it is cyclic, the pi orbitals of the carbons all lie in the same plane, it satisfies Huckels rule, and is fully conjugated.