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

References

External links

Weisstein, Eric W. "Prism". MathWorld.