  Aims. The data set of the long-term XMM-Newton monitoring program of HD 81809
is analyzed to study its X-ray cycle, to investigate if the latter is related
to the chromospheric one, to infer the structure of the corona of HD 81809, and
to explore if the coronal activity of HD 81809 can be ascribed to phenomena
similar to the solar ones and, therefore, considered an extension of the solar
case. Methods. We analyze the observations of HD 81809 performed with
XMM-Newton with a regular cadence of 6 months from 2001 to 2016 and
representing one of the longest available observational baseline ($\sim 15$~yr)
for a solar-like star with a well-studied chromospheric cycle (with a period of
$\sim 8$~yr). We investigate the modulation of coronal luminosity and
temperature and its relation with the chromospheric cycle. We interpret the
data in terms of a mixture of solar-like coronal regions, adopting a
methodology originally proposed to study the Sun as an X-ray star. Results. The
observations show a well-defined regular cyclic modulation of the X-ray
luminosity that reflects the activity level of HD 81809. The data covers
approximately two cycles of coronal activity; the modulation has an amplitude
of a factor of $\sim 5$ (excluding evident flares, as in the June 2002
observation) and a period of $7.3\pm 1.5$~yr, consistent with that of the
chromospheric cycle. We demonstrate that the corona of HD 81809 can be
interpreted as an extension of the solar case and it can be modeled with a
mixture of solar-like coronal regions along the whole cycle. The activity level
is mainly determined by a varying coverage of very bright active regions,
similar to cores of active regions observed in the Sun. Evidence of unresolved
significant flaring activity is present especially in proximity of cycle
maxima.

Solar and Stellar Astrophysics