A glass roof light is made as a flat panel…

A glass roof light is made as a flat panel. In the drawing of the panel, $x$ and $y$ are in metres. The top edge of the panel is the parabola $y = 8 - x^2$, and the bottom edge is the V-shaped line $y = 2|x|$. The panel is the region between the V and the parabola, and it is symmetric about the $y$-axis. A steel beam runs along the vertical line $x = 1$. The part of the panel to the right of the beam is tinted. Find the value of $x$ at which the parabola meets the right arm of the V. Then find the total area of the panel in square metres. Finally find the area of the tinted part, between the beam and the right edge of the panel, in square metres. Give both areas to two decimal places. The supplier charges by area, so the designer needs good accuracy. Do not round any number until the last step.