Answer
Domain: $(0,8)$ or $0\lt x\lt8$
Work Step by Step
$x+2y-8=0$
$2y=8-x$
$y=4-\frac{x}{2}$
Since $A=xy$, we must have that $x\gt0$ and $y\gt0$.
$y\gt0$
$4-\frac{x}{2}\gt0$
$-\frac{x}{2}\gt-4$
$\frac{x}{2}\lt4$
$x\lt8$
So, we must have that $x\gt0$ and $x\lt8$. That is, $0\lt x\lt8$.
