Folding a Rectangle: Area and Quadratic Equation

The diagram represents a piece of rectangular paper \(ABCD\) which has been folded along the line \(EC\) so that \(D\) has moved to \(F\).

The length of \(AB\) is \(\left( 4x+2 \right)\)cm, \(BC\) is \(\left( 3x-1 \right)\) cm and \(ED\) is \(2\) cm.

1. Write down, in terms of \(x\), and expression for the area of rectangle \(ABCD\).
2. Write down, in terms of \(x\), an expression for the area of the triangle \(CDE\).
3. Given that the area of the shaded region \(ABCFE\) is \(570\) cm\(^{2}\), form an equation in \(x\) and show that it simplifies to \(2{{x}^{2}}-x-96=0\).
4. Solve the equation \(2{{x}^{2}}-x-96=0\), giving your answers correct to three decimal places.
5. Hence, find the area of the folded paper \(CEF\), giving your answer correct to \(2\) decimal places.