Final answer:
Without additional information, we cannot directly calculate the area of the pyramid's square base from the total area of its triangular faces. The area of the base must be less than the total area of the triangular faces. The most probable answer is 20 cm², given the options, provided the triangular faces are equal in area.
Step-by-step explanation:
The student's question about the area of a pyramid's base, given the total area of its triangular faces, involves understanding geometric relationships between the shapes. The key information is that the total area of the triangular faces is 80 cm². To find the area of the square base, one would need information about the pyramid's dimensions, such as slant height or the height of each triangular face. Since we are not provided with this information, the question seems to be impossible to answer directly. However, it's important to realize that the area of a square base cannot be the same as the total area of the triangular faces. Therefore, the area of the square base cannot be 80 cm², which corresponds to option d. If we were to choose from the options given, with the assumption that the area of the base must be one of the remaining options and that the triangular faces are equal in area, option b) 20 cm² is the most probable, as it allows for identical triangular faces with an area equal to a quarter of the total area provided.