Final answer:
Without specific dimensions of the rectangular prism, it is impossible to determine which statements about the area of its faces are true. Rectangular prisms have opposite faces with equal areas, and the area is calculated as length times width. For accurate cross-sectional areas, Block A would have an area of 2L², and Block B would have an area of 4L² if 'L' represents the same unit length for both.So, the correct option is
C) Two of the faces have an area of 40 ft²
Step-by-step explanation:
To determine which statements about the area of the faces of a rectangular prism are true, we need to have the dimensions of the prism or enough information to deduce the area of each face. However, there is no specific information given in the question regarding the dimensions of the rectangular prism, making it impossible to confirm which of the statements A to E is true.
That said, we can discuss general properties of rectangular prisms. In a rectangular prism, opposite faces have equal areas because they have the same dimensions. Therefore, if we know the area of one face, we then know the area of its opposite face as well. Also, the formula for calculating the area of a rectangle is length times width (A = lw). If a student has incorrect information, such as the cross-sectional area of Block A being incorrect as '21²' or Block B being '41²', it is important to clarify that these expressions are not valid and should likely represent the squares of certain lengths which are not provided.
Considering the correct calculation of the cross-sectional area for a rectangular face with lengths L and 2L, it should be 2L² for Block A and 4L² for Block B, with Block B's area being twice that of Block A assuming the 'L' represents the same unit length for both blocks. However, without the specific values for L, we cannot calculate the exact area.So, the correct option is
C) Two of the faces have an area of 40 ft²