In planetary motion the areal velocity of position vector of a planet depends on angular velocity (r) and the distance of the planet from sun (r). If so the correct relation for areal velocity is :

dA/dt ∝ ω r dA/dt ∝ ω2 r dA/dt ∝ ω r2 dA/dt ∝ √ωr

dA/dt ∝ ω r2

\(\frac{dA}{dt} = \frac{L}{2m}\)    =\(\frac{mvr}{2m}\)    =\(\frac{1}{2}\omega r^2\) [As Angular momentum L = mvr and v = rω]  \(\Rightarrow \frac{dA}{dt} \propto \omega r^2\)