Another Problem using Heron's

Geometry Level 3

Let $\triangle ABC$ have a circle inscribed inside of it such that the circle is tangent at points $X$ , $Y$ , and $Z$ along sides $AB$ , $AC$ , and $BC$ , respectively. Let $AX=3$ , $BZ=4$ , and $CY=5$ . Find the area of $\triangle ABC$ .

If your answer can be expressed as $a\sqrt{b}$ where $a$ and $b$ are positive integers with $b$ squarefree, find $a+b$ .