If we let the surface of the water be the x-axis and bisect it with the y-axis,
then perhaps we copuld find the equation of the line which represents the
side of the plate.
The bottom right corner will have coordinates (10,-8) and the top right corner will have coordinates (6,0)
Using these two points to find our line equation we get or
The depth is -y and the length of the region at y is
So, we can set up the integral:
You could also try similar triangles and see if you get the same thing.