A pentagonal pyramid is pyramid having a pentagonal base. The edge length 
and slant height 
of a pentagonal pyramid with regular base of side length 
are given by
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the height and 
is the length of a side of the base. It has surface area and volume
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |
The regular pentagonal pyramid having equilateral triangles as faces so that all its edges are of the same length is Johnson solid 
.
For the equilateral pentagonal pyramid with edge length 
, the slant height is
 |
(5)
|
and the surface area and volume are
 |  |  |
(6)
|
 |  |  |
(7)
|
