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]