Pentagonal Pyramid
A pentagonal pyramid is pyramid having a pentagonal base. The edge length 👁 e
and slant height 👁 s
of a pentagonal pyramid with regular base of side length 👁 a
are given by
where 👁 h
is the height and 👁 a
is the length of a side of the base. It has surface area and volume
| 👁 S | 👁 = | 👁 (5a(a+sqrt(a^2+4(5-2sqrt(5))h^2)))/(4sqrt(5-2sqrt(5))) |
(3)
|
| 👁 V | 👁 = | 👁 1/(12)a^2hsqrt(25+10sqrt(5)). |
(4)
|
The regular pentagonal pyramid having equilateral triangles as faces so that all its edges are of the same length is Johnson solid 👁 J_2
.
For the equilateral pentagonal pyramid with edge length 👁 a
, the slant height is
| 👁 s=1/2sqrt(3)a, |
(5)
|
and the surface area and volume are
See also
Johnson Solid, Pentagon, Pentagonal Prism, Pyramid, Regular Pyramid, Square Pyramid, Triangular PyramidExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Pentagonal Pyramid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PentagonalPyramid.html