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.