The length of a rectangle is increasing at a rate of $5c\frac{m}{s}$ and its width is increasing at a rate of $4c\frac{m}{s}.$ When the length is $11cm$ and the width is $4cm,$ how fast is the area of the rectangle increasing $($in $c\frac{m}{2}s)?$

$c\frac{m^2}{s}$