Final answer:
The problem involves calculating the surface area of a triangular prism box and then finding its material cost per its surface area. Specific measurements for the box are required to perform the calculations.
Step-by-step explanation:
The question pertains to finding the total surface area of a chocolate box shaped as a triangular prism and then calculating the cost of the materials for one box based on the surface area price. To find the total surface area of a triangular prism, we need to calculate the area of all faces - which includes both triangular bases and the three rectangles that connect them. The formula for the area of a triangle is ½ × base × height.
The question does not provide the dimensions of the triangular base, so we will assume generic variables, 'b' for base and 'h' for the height of the triangle. The area of each triangular base would then be ½ bh. If 'l' is the length of the prism, then the area of the three rectangular sides would sum up to 'l' multiplied by the perimeter of the triangle's base. To calculate the cost of one box, we multiply the total area by the cost per square centimeter, in this case, $0.01. The important thing to remember is to keep all units consistent; since the cost is given per square centimeter, all measurements must also be in centimeters.