Let A and B be the two points of intersection of the line y+5=0 and the mirror image of the parabola y^2=4 x with respect to the line x+y+4=0. If d…

Let A and B be the two points of intersection of the line $\displaystyle y+5=0$ and the mirror image of the parabola $\displaystyle y^2=4 x$ with respect to the line $\displaystyle x+y+4=0$. If d denotes the distance between A and B, and a denotes the area of $\displaystyle \Delta \mathrm{SAB}$, where S is the focus of the parabola $\displaystyle y^2=4 x$, then the value of $\displaystyle (\mathrm{a}+\mathrm{d})$ is $\displaystyle \_\_\_\_$.