An irrigation channel on a farm has a cross-section shaped like the parabola y = x²…

An irrigation channel on a farm has a cross-section shaped like the parabola $y = x^2$. Here $x$ and $y$ are measured in decimetres (dm), and the origin is at the lowest point of the channel floor. When the channel is full, the water surface is the line $y = 9$. The farmer wants to paint a mark on the channel wall. When the water reaches the mark, the cross-section of the water should be exactly half the cross-section of the full channel. Find the area of the cross-section of the full channel. Then let the water surface be the line $y = k$, and write the area of the water cross-section in terms of $k$. Set this equal to half of the full area, and solve for $k$. Give the height of the mark above the channel floor in decimetres, to two decimal places. Water flows evenly along the whole length of the channel, so only the cross-section matters. Do not round any number until the last step.