  We present the photometric analysis of six short-period systems (EI Oct, V336
TrA, NX Boo, V356 Boo, PS Boo, and V2282 Cyg). This is the first photometric
analysis of these systems except for V336 TrA. Observations were conducted for
27 nights at three observatories in the northern and southern hemispheres. We
calculated a new ephemeris for each of the systems using our minimum times and
additional literature. The Markov Chain Monte Carlo (MCMC) approach was used to
determine the eclipse timing variation trends of the systems. We found a likely
orbital growth for V336 TrA and PS Boo; four other systems show a linear trend
in orbital period changes, which is most likely due to the accumulation of
measurement errors in their linear ephemeris parameters. The light curve
analysis was performed using the Physics of Eclipsing Binaries (PHOEBE) 2.3.59
version code with the MCMC approach. The absolute parameters of the systems
were calculated by using the Gaia Early Data Release 3 (EDR3) parallax. The
positions of the systems were also depicted on the Hertzsprung-Russell (H-R)
and $logJ_0-logM$ diagrams. According to a sample, we were able to present
relations for the mass-radius (M-R) relationships of contact binary systems.
There is also a strong relationship between the mass ratio and the radius ratio
in the W UMa systems for which we also provided a new relation. We compared the
M-R updated relationships in this study with seven systems in other studies
obtained using the spectroscopic method. In addition, we estimated some of the
absolute parameters for 1734 EW systems, based on the new relationships.
