Reckoning / Shape / Square pyramid
Solid · Prisms and pyramids
Square pyramid
A square base with four triangles meeting at the apex above its centre.
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Dimensions
Results
volume V
slant height l
surface area S
Formulas
Any pyramid holds one third of the prism with the same base and height. A cube can be cut into three equal square pyramids that share one corner of the cube as their apex.
Checked: the V, S formula agrees with a Monte Carlo measurement of the shape itself, made from its geometric definition, every time the site is built.
Topology lens
Topologically a ball. Its surface has V = 5 vertices, E = 8 edges and F = 5 faces, and V − E + F = 2, as for every convex polyhedron (Euler, 1758). More on the lens.