How is the volume of a triangular pyramid related to the area of its base?

The volume of a triangular pyramid is indeed directly proportional to the area of its base. To understand this relationship, consider how the volume of a triangular pyramid is calculated. The formula for the volume is given by:

[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} ]

In this formula, as the area of the base increases, while the height remains constant, the volume of the pyramid will also increase. This demonstrates direct proportionality; if the area of the base doubles, then the volume will also double, assuming the height stays the same.

It's also important to recognize that the height plays a role in determining the volume, but this does not negate the fact that the volume is directly influenced by the base area. Understanding this proportional relationship allows one to effectively compute the volume for various triangular pyramids, adjusting for changes in either base area or height. Therefore, option A accurately captures this fundamental relationship in geometry.