What is the relationship between the volume of a prism and a pyramid with congruent base areas and heights?

The relationship between the volume of a prism and a pyramid with congruent base areas and heights can be understood by first understanding the formulas for finding their volumes.

The volume of a prism can be calculated using the formula:

Volume of a prism = Base area * Height

The base area is the area of the base of the prism, and the height is the perpendicular distance between the base and the top face.

For a pyramid with a congruent base area and height, the volume can be calculated using the formula:

Volume of a pyramid = (1/3) * Base area * Height

Again, the base area is the area of the base of the pyramid, and the height is the perpendicular distance between the base and the top point (apex) of the pyramid.

Now, coming back to the relationship between the volume of a prism and a pyramid with congruent base areas and heights:

Since both the prism and the pyramid have congruent base areas and heights, we can write the equations for their volumes as follows:

Volume of prism = Base area * Height

Volume of pyramid = (1/3) * Base area * Height

From these formulas, we can see that the volume of the pyramid is one-third of the volume of the prism with the same base area and height.

So, in conclusion, the volume of a pyramid with a congruent base area and height is one-third of the volume of a prism with the same base area and height.