  The harvest of exoplanet discoveries has opened the area of exoplanet
characterisation. But this cannot be achieved without a careful analysis of the
host star parameters. The system of HD219134 hosts two transiting exoplanets
and at least two additional non-transiting exoplanets. We used the VEGA/CHARA
interferometer to measure the angular diameter of HD219134, leading to a
stellar radius of $R_{\star}=0.726\pm0.014 R_{\odot}$. We also derived the
stellar density from the transits light curves ($\rho_{\star}=1.82\pm0.19
\rho_{\odot}$), which finally gives a direct estimate of the mass
($M_{\star}=0.696\pm0.078 M_{\odot}$) with a correlation of 0.46 between
$R_{\star}$ and $M_{\star}$. This new mass is smaller than that derived from
the C2kSMO stellar evolutionary model, which provides a mass range of
0.755$-$0.810 ($\pm 0.040$) $M_{\odot}$. This allows us to infer the mass,
radius and density of the two transiting exoplanets of the system. We then use
an inference model to obtain the internal parameters of these two transiting
exoplanets. Moreover, we find that planet $b$ and $c$ have smaller radii than
previously estimated ($1.500\pm0.057$ and $1.415\pm0.049 R_{\oplus}$,
respectively); this clearly puts these planets out of the gap in the
exoplanetary radii distribution and validates their super-Earth nature. Planet
$b$ is more massive than planet $c$, but possibly less dense. We investigate
whether this could be caused by partial melting of the mantle and find that
tidal heating due to non-zero eccentricity of planet $b$ may be powerful
enough. The system of HD219134 constitutes a very valuable benchmark for both
stellar physics and exoplanetary science. The direct determination of the
stellar density, radius and mass should be more extensively applied to provide
accurate exoplanets properties and calibrate stellar models.
