The curves are y² = 9x and y = x

Solving the above equations, we have

\[\begin{array}{*{35}{l}}

{{x}^{2}}~=\text{ }9x\text{ }\Rightarrow \text{ }{{x}^{2}}~\text{ }-9x\text{ }=\text{ }0  \\

x\left( x\text{ }-\text{ }9 \right)\text{ }=\text{ }0  \\

So,\text{ }x\text{ }=\text{ }0,\text{ }9  \\

\end{array}\]

Now, the required area is

Therefore, the required area is 27/2 sq. units.