Why area swept by the planet=ΔA=1/2(r cross vΔt)

Dear Student ,

let the speed be v and the radius be r of the planet  .
$$\begin{gathered} angular dispacement in ∆t time \\ \theta =\frac{v∆t}{r} \\ area cover by the radius vector \\ ∆A=\frac{\theta }{2\mathrm{\pi }}\left({\mathrm{\pi r}}^2\right)=\frac{\frac{v∆t}{r}}{2}\left(r^2\right)=\frac{rv∆t}{2} \\ Regards \end{gathered}$$