2008 TYS

The diagram shows the curve with equation $y={{x}^{2}}$. The area of the region bounded by the curve, the lines $x=1$, $x=2$ and the $x$-axis is equal to the area of the region bounded by the curve, the lines $y=a$, $y=4$ and the $y$-axis, where $a<4$. Find the value of $a$.[4]