  We investigate the statistics of the convex hull for a single run-and-tumble
particle in two dimensions. Run-and-tumble particle, also known as persistent
random walker, has gained significant interest in the recent years due to its
biological application in modelling the motion of bacteria. We consider two
different statistical ensembles depending on whether (i) the total number of
tumbles $n$ or (ii) the total observation time $t$ is kept fixed. Benchmarking
the results on perimeter, we study the statistical properties of the area of
the convex hull for RTP. Exploiting the connections to extreme value
statistics, we obtain exact analytical expressions for the mean area for both
ensembles. For fixed-$t$ ensemble, we show that the mean possesses a scaling
form in $\gamma t$ (with $\gamma$ being the tumbling rate) and the
corresponding scaling function is exactly computed. Interestingly, we find that
it exhibits crossover from $\sim t^3$ scaling at small times $\left( t \ll
\gamma ^{-1} \right)$ to $\sim t$ scaling at large times $\left( t \gg \gamma
^{-1} \right)$. On the other hand, for fixed-$n$ ensemble, the mean expectedly
grows linearly with $n$ for $n \gg 1$. All our analytical findings are
supported with numerical simulations.
