Assume the base of $\text{Δ}S{S}^{\prime }B$ is $S{S}^{\prime }$, then 
base $=S{S}^{\prime }=2ae$
height $=\frac{1}{2}\left(\frac{2b^2}{a}\right)=\frac{\mathrm{length} \mathrm{of} \mathrm{latus} \mathrm{rectum}}{2}$
$\Rightarrow \text{area of Δ}BS{S}^{\prime }=\frac{1}{2}\left(2ae\right)\left(\frac{b^2}{a}\right)$$=b^{2}e$
Now, equation of the ellipse is $\frac{{\left(x-3\right)}^2}{25}+\frac{{\left(y+2\right)}^2}{16}=1$
$\Rightarrow a^2=25,b^2=16,e^2=\frac{9}{25}$
$\Rightarrow b^{2}e=16\times \frac{3}{5}=\frac{48}{5}$

Hence, area of $\text{Δ}BS{S}^{\prime }$$=\frac{48}{5}$ sq. units