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)
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(2)
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where is the height and is the length of a side of the base. It has surface area and volume
(3)
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(4)
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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)
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and the surface area and volume are
(6)
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(7)
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