The curves are y² = 4x … (i) and x² = 4y … (ii)

On solving the equations, we get

From (ii),

y = x²/4

Putting value of y in (i), we have

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

{{\left( {{x}^{2}}/4 \right)}^{2}}~=\text{ }4x  \\

{{x}^{4}}/16\text{ }=\text{ }4x  \\

{{x}^{4}}~=\text{ }64x  \\

{{x}^{4}}~\text{ }-64x\text{ }=\text{ }0  \\

So,\text{ }x\text{ }=\text{ }0,\text{ }4  \\

\end{array}\]

Now, the required area is the shaded region