Prove that the curves ${\mathrm{y}}^2=4\mathit{x}$ and ${\mathit{x}}^2=4\mathrm{y}$ divide the area of the square bounded by sides $\mathit{x}=0,\mathit{x}=4,\mathrm{y}=4$ and $\mathrm{y}=0$ into three equal parts.
OR
Using integration, find the area of the triangle whose vertices are $\left(2,3\right),\left(3,5\right)$ and $\left(4,4\right)$.