Answer: See below.
Do you have a drawing of the net? That would be more helpful, I am not sure where the measurements go.
For your questions:
To find the surface area, you find the area of each individual shape in the net. Then, you add them together. For the rectangles, it is BH. For the triangles, it is BH/2.
To find the lateral area, you just need to find the combined area of the three rectangles.