Imagine yourself as the engineer of a heart$-$lung machine, ready to oxygenate blood with the precision of a maestro using silicone rubber as your secret weapon. But wait, there's more! Armed with the experimental oxygen permeability value for silicone rubber $(6\mathrm{.}50{10}^{-7}ml$ oxygen $($STP$)/($s$.$cm$^2.($:$cmH\frac{g}{m}m\})$ and battling pressure differentials on one side, $50mmHg$ on the blood side$),$ all while contending with a thickness of $0\mathrm{.}275mm.$ Now, here's the plot twist: the oxygen demand per adult is a whopping $555ml$ oxygen $($STP$)$ per minute. Your challenge, should you accept it$,$ is to calculate the total membrane area required to meet this oxygen extravaganza.

So$,$ gear up your brain cells and let's dive into the oxygenating adventure! Calculate that membrane area in $m^2$ and let's turn the tables on oxygen deficiency!

Round your answer to $2$ decimal places.