## Challenge 350: Trapezium Trial

The parabola with equation y = 4 – x^{2} intersects the positive x-axis at Q and the y-axis at P.

The straight line L_{1} has gradient m and passes through P, and the straight line L_{2} which passes through Q, is parallel to L_{1}.

L_{1} intersects the parabola at S and L_{2} intersects the parabola at R.

Given that m > 0, find an expression for the area of the trapezium PQRS in terms of m.

What if m __<__ 0?