The angular momentum of a planet of mass $$M$$ moving around the sun in an elliptical orbit is $$\vec{L}$$. The magnitude of the areal velocity of the planet is :

The angular momentum of the planet about the sun is $$L = M v_\perp r$$, where $$v_\perp$$ is the component of velocity perpendicular to the radius vector and $$r$$ is the distance from the sun.

The areal velocity is the rate at which the radius vector sweeps out area: $$\frac{dA}{dt} = \frac{1}{2} r \, v_\perp$$.

Since $$L = M r \, v_\perp$$, we get $$r \, v_\perp = \frac{L}{M}$$. Substituting into the areal velocity expression: $$\frac{dA}{dt} = \frac{1}{2} \cdot \frac{L}{M} = \frac{L}{2M}$$.