To determine the volume of a pyramid, which formula is used?

The formula for determining the volume of a pyramid is given by ( V = \frac{1}{3} \times \text{(area of base)} \times \text{(height)} ). This formula is derived from the concept that the volume of a pyramid is one-third of the product of the area of its base and its height. This relationship holds true because a pyramid can be thought of as a three-dimensional shape with a pointed top, where each cross-section parallel to the base reduces in area as it moves upward toward the apex.

The area of the base is crucial because it provides the foundational space over which the height acts. The height is the perpendicular distance from the apex to the base. By multiplying the area of the base by the height, you effectively calculate the volume of a prism that would encompass the pyramid. The division by three accounts for the fact that a pyramid occupies only a fraction of that volume, reflecting the relationship between the shapes.

Other choices, while related to geometric concepts, do not correctly represent the volume of a pyramid. For instance, one choice provides the formula for the area of a triangle or rectangle, which does not pertain to volume calculations, while another refers to a formula that may compute area or