A rectangular prism has a volume of 252 If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
We know that the volume of a rectangular pyramid is given by:
$V_\text{pyramid} = \frac{1}{3} A_\text{base} \times h$
where $A_\text{base}$ is the area of the base and $h$ is the height.
Since the base and height of the pyramid are congruent to the base and height of the rectangular prism, their areas are equal. So, we can write:
$A_\text{base} \times h = V_\text{prism}$
We are given that $V_\text{prism} = 252$. Now, we will substitute this into the volume formula for the pyramid:
$V_\text{pyramid} = \frac{1}{3} (252)$
$V_\text{pyramid} = 84$
The volume of the pyramid is 84 cubic units.