A ranger in Cornwall is protecting a sand dune from walkers…

A ranger in Cornwall is protecting a sand dune from walkers. She has surveyed its cross-section and found that it follows the curve $y = 5\sin\dfrac{\pi x}{10}$. Here $x$ is the distance in metres from the sea end, and $y$ is the height in metres, for $0 \le x \le 10$. New grass will be planted in two stages. The part nearest the sea is planted first by one team, and the rest is planted by a second team in the following season. The ranger wants a fence post at the position $x = c$ to mark the boundary. The area of the cross-section to the left of the post must be one quarter of the area of the whole cross-section. Then the two teams share the work in the proportions $1$ to $3$. First find the area of the whole cross-section, in square metres. Then find the position $c$ of the post, in metres.