What is the formula for the volume of a pyramid?

The formula for the volume of a pyramid is indeed 1/3 times the area of the base times the vertical height. This formula is derived from the more general concept of the volume of three-dimensional shapes.

A pyramid can be thought of as a three-dimensional shape with a polygonal base and triangular faces that converge at a point (the apex). To find the volume of such shapes, we consider how much space they occupy. The area of the base gives us the 'footprint' of the pyramid, and multiplying it by the vertical height (the perpendicular distance from the base to the apex) helps in determining how tall the pyramid is. Since a pyramid occupies only a third of the space that a prism with the same base area and height would occupy, we multiply the product of the area and height by one-third.

In contrast, the other options do not correctly describe the volume of a pyramid. The area of the base multiplied by the height does not account for the division by three, which is essential for pyramids specifically. Similarly, base multiplied by height multiplied by length does not apply to pyramids when considering their triangular sides and overall volume. Lastly, the option with 2/3 is incorrect because, similar to the area