$$\begin{gathered} Theareaofthetriangleformedbythelines{x}^2-9xy+18y^2=0and \\ theliney-1=0is\left(insq.units\right) \end{gathered}$$

$\begin{array}{l}Givenlines{x}^2-9xy+18y^2=0\\ Comparingwitha{x}^2+2hxy+b{y}^2=0\\ a=1,2h=-9,b=18\\ andy-1=0\\ comparingwithlx+my+n=0\\ l=0,m=1,n=-1\end{array}$

$\begin{array}{l}Areaof{\Delta }^{le}=\frac{n^2\sqrt{h^2-ab}}{\left|a{m}^2-2hlm+b{l}^2\right|}\\ =\frac{1\sqrt{\frac{81}{4}-18}}{\left|1{\left(1\right)}^2+9\left(0\right)\left(1\right)+18{\left(0\right)}^2\right|}\\ =\frac{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{1}\\ =\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\end{array}$