Heptagonal prism

In geometry, the heptagonal prism is a prism with heptagonal base. This polyhedron has 9 faces (2 bases and 7 sides), 21 edges, and 14 vertices.

Area

The area of a right heptagonal prism with height h {\displaystyle h} and with a side length of L {\displaystyle L} and apothem a p {\displaystyle a_{p}} is given by:

A = 7 L ⋅ ( a p + h ) {\displaystyle A=7L\cdot (a_{p}+h)}

Volume

The volume is found by taking the area of the base, with a side length of L {\displaystyle L} and apothem a p {\displaystyle a_{p}}, and multiplying it by the height h {\displaystyle h}, giving the formula:

V = 7 2 ⋅ h ⋅ L ⋅ a p {\displaystyle V={\frac {7}{2}}\cdot h\cdot L\cdot a_{p}}

This formula also works for the oblique prism due to the Cavalieri's principle.

Images

The heptagonal prism can also be seen as a tiling on a sphere:

Related polyhedra

External links

• Weisstein, Eric W. . MathWorld.