  We construct a sample of nearly 30,000 main-sequence stars with 4500K
$<T\rm_{eff}<$ 5000K and stellar ages estimated by the chromospheric
activity$-$age relation. This sample is used to determine the age distribution
in the $R-Z$ plane of the Galaxy, where $R$ is the projected Galactocentric
distance in the disk midplane and $Z$ is the height above the disk midplane. As
$|Z|$ increases, the percentage of old stars becomes larger. It is known that
scale-height of Galactic disk increases as $R$ increases, which is called
flare. A mild flare from $R$ $\sim$ 8.0 to 9.0 kpc in stellar age distribution
is found. We also find that the velocity dispersion increases with age as
confirmed by previous studies. Finally we present spiral-shaped structures in
$Z-\upsilon_{Z}$ phase space in three stellar age bins. The spiral is clearly
seen in the age bin of [0, 1] Gyr, which suggests that a vertical perturbation
to the disk probably took place within the last $\sim$ 1.0 Gyr.
