1. Problem statement: A swimming pool is 20 ft wide and 40 ft long and its cross-section has shallow depth 3 ft and deepest depth 9 ft, with the cross-section vertices at $ (0,9), (0,6), (6,0), (18,0), (34,6), (40,6), (40,9)$. 2. Coordinate choice: Place the deepest bottom at $y=0$ and let $h$ be the water depth at the deepest point so the water fills $0\le y\le h$. 3. Left boundary: For a horizontal slice at height $y$ the left wall is the line from $(0,6)$ to $(6,0)$, so $x_L(y)=6-y$ for $0\le y\le6$, and $x_L(y)=0$ for $6