geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

, the heptagonal prism is a

prism Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...

with

heptagon In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of ''septua-'', a Latin-derived numerical prefix, rather than '' hepta-'', a Greek-derived nu ...

al base. This

polyhedron In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on ...

has 9 faces, 21 edges, and 14 vertices..

Area

The

area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an ope ...

of a right heptagonal prism with height

h

and with a side length of

L

and

apothem The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides. T ...

a_p

is given by: :

A = 7L\cdot (a_p + h)

Volume

The

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...

is found by taking the area of the base, with a side length of

L

and apothem

a_p

, and multiplying it by the height

h

, giving the formula: :

V = \frac\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: : Spherical heptagonal prism

Related polyhedra

References

External links

* Prismatoid polyhedra {{Polyhedron-stub