If you stretch the surface out so that it lays "flat" you can see that it is a rectangle. So the surface area is just the width (.5 m) times the length. The length of the rectangle is the arc length of the function which describes the shape of the surface in the z/x plane (I am taking the positive z-axis to point "up", positive y-axis points "out" of the image, positive x-axis in the direction of the water flow)
If you are not given the function I guess we are to assume it behaves like a cosine function (seems so). It osccilates 3.5 periods in 2 meters and has an amplitude of .25m, with this information we can construct the cosine function that describes the shape.
Then the length of this curve is given by:
So the area of the upper surface is approximately . It appears that the same object is the lower surface as well, so the total area of the upper and lower surfaces is just .
Are we to assume there are edges as well? If so it appears that we are assuming a constant "height" (distance between the two surfaces) of .02 meters? Then the area of each edge is just
Which leads to a total surface area of . What do you think?