Answer: 235.8 square km
Explanation
The base or floor is a hexagon. We ignore this when determining the lateral area because the lateral sides are basically the walls.
So we only consider the 6 triangular panels.
Each panel is congruent so let's focus on one particular wall panel. Any particular triangle has base 6 km and height 13.1 km
area = 0.5*base*height = 0.5*6*13.1 = 39.3 square km.
That's the area of one triangle, but there are 6 identical copies or clones. So we have 6*39.3 = 235.8 square km of total lateral surface area.
Note: The 5.2 km measurement was put in there as a distraction. It's never used.
