  We prove Strichartz inequalities for the wave and Schr\"odinger equations on
noncompact surfaces with ends of finite area, i.e. with ends isometric to $
\big( (r_0,\infty) \times {\mathbb S}^1 , dr^2 + e^{- 2 \phi (r)}d \theta^2
\big) $ with $ e^{-\phi} $ integrable. We prove first that all Strichartz
estimates, with any derivative loss, fail to be true in such ends. We next show
for the wave equation that, by projecting off the zero mode of $ {\mathbb S}^1
$, we recover the same inequalities as on $ {\mathbb R}^2 $. On the other hand,
for the Schr\"odinger equation, we prove that even by projecting off the zero
angular modes we have to consider additional losses of derivatives compared to
the case of closed surfaces; in particular, we show that the semiclassical
estimates of Burq-G\'erard-Tzvetkov do not hold in such geometries. Moreover
our semiclassical estimates with loss are sharp.
