Primary Mathematical Formula
$$V = \frac{5}{12} \tan(54^\circ) a^2 h$$
Frequently Asked Questions
How do you calculate the volume of a pentagonal pyramid?
Calculate the pentagonal base area, multiply it by the perpendicular height, and divide by 3.
What is the formula for pentagonal pyramid volume?
The formula is $V = \frac{1}{3} B h$, where $B$ is the pentagon's area and $h$ is the pyramid's perpendicular height.
How do you calculate the volume of a regular pentagonal pyramid?
For a regular pentagon, calculate the base area using $B = \frac{1}{2} P a = \frac{5}{4} s^2 \cot(36^\circ)$, where $P$ is the perimeter, $s$ is the side length, and $a$ is the apothem. Then multiply by the pyramid height and divide by 3: $V = \frac{5}{12} s^2 \cot(36^\circ) h$.
How many faces does a pentagonal pyramid have?
A pentagonal pyramid has six faces: one pentagonal base and five triangular side faces.
Can I calculate a pentagonal pyramid's volume using only its side length?
No. You also need the perpendicular height or enough additional geometric measurements (such as face slant height) to determine it.