The area of the region bounded by $y=\left|x-2\right|,x=3$ and X – axis is

$y=\left|x-2\right|$

$x-y-2=0$

$x+y-2=0$

By solving $B=\left(1,2\right)$

                     $A=\left(2,0\right)$

                      $C=\left(1,0\right),D=\left(3,1\right)$

$R.A=2\left(Areaof\Delta ABC\right)$

      $=2\left(\frac{1}{2}\left(1\right)1\right)=1$