Final answer:
To find the base area of the pentagonal prism, divide the volume (387 units³) by the height (12.9 units), resulting in a base area of 30 units², which is option a. Option a is correct.
Step-by-step explanation:
The student's question is related to finding the base area of a pentagonal prism given its height and volume. To solve for the base area of the prism, we must divide the volume by the height. Given the volume of the prism is 387 units³ and the height is 12.9 units, the base area can be calculated as follows:
Base Area = Volume / Height
Base Area = 387 units³ / 12.9 units
Base Area = 30 units².
The volume of a pentagonal prism can be calculated by multiplying the area of the base by the height. The formula is:
V = A * h
To find the area of the base, we can divide the total volume by the height:
A = V / h
Substituting the values given:
A = 387 / 12.9 = 30
Therefore, the area of the base of the pentagonal prism is 30 units.
This means the correct answer is a. 30 units, representing the area of the pentagonal base of the prism.