The planes parallel to the edge AD are: adeh, hefg, gfbd, ABCD. Let AD=x, then the areas of these four surfaces are 5x, 3x, 5x and 3x respectively. Because the sum of the areas of these four surfaces is 32, it is 16x = 32 and x = 2, so the surface area of this cuboid is 32+2×3×5=62.