Q: What is the formula for the height of a regular hexagonal three dimensional structure?

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A polyhedron is a simply connected 3-dimensional shape whose faces are all regular polygons. A hexagonal pyramid is a special case in which one face is a hexagon and six faces are triangles.

Assuming it's a regular hexagon, V= 6√3 x2h where x is one of the sides of the hexagonal base and h is the height of the box.

Irregular.

Because regular hexagonal shapes are able to tessellate leaving no gaps or overlaps.

First we assume it is a regular hexagon meaning all the angles are the same and the sides are the same length. Recalling that a regular hexagon can be broken up into 6 triangles, we find the area of the hexagon by finding the area of one triangle and multiply by six. (recall the area of triangle is Height x 1/2 Base ) You can also find the area of a hexagon using the formula Area==ap/2 where a is the apothem and p is the perimeter. But that just gives you the area of the 2 dimensional base, not the volume. To calculate the volume, multiply the area found above by the height of the hexagonal container.

Related questions

A polyhedron is a simply connected 3-dimensional shape whose faces are all regular polygons. A hexagonal pyramid is a special case in which one face is a hexagon and six faces are triangles.

Assuming it's a regular hexagon, V= 6√3 x2h where x is one of the sides of the hexagonal base and h is the height of the box.

Octagon. * * * * * An octagon is 2-dimensional. The regular 3-d shape (all faces the same) is the octahedron, but a hexagonal prism also has 8 faces.

Irregular.

hexagonal prism In geometry, the hexagonal prism is a prism with hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices. Since it has 8 faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces. https://en.wikipedia.org/wiki/Hexagonal_prism#/media/File:Hexagonal_prism.png

Because regular hexagonal shapes are able to tessellate leaving no gaps or overlaps.

First we assume it is a regular hexagon meaning all the angles are the same and the sides are the same length. Recalling that a regular hexagon can be broken up into 6 triangles, we find the area of the hexagon by finding the area of one triangle and multiply by six. (recall the area of triangle is Height x 1/2 Base ) You can also find the area of a hexagon using the formula Area==ap/2 where a is the apothem and p is the perimeter. But that just gives you the area of the 2 dimensional base, not the volume. To calculate the volume, multiply the area found above by the height of the hexagonal container.

A

The regular dodecahedron is the 3-dimensional analog of a regular pentagon. In other words, it is a three-dimensional pentagon.

Solid water resembles a crystalline structure, with its molecules forming a regular pattern known as a hexagonal lattice. This lattice arrangement gives ice its hardness and transparent appearance.

Boron has a unique crystal structure called rhombohedral boron, which consists of B12 icosahedra linked together in a three-dimensional network without a regular repeating pattern.

A hexagonal prism is a polyhedron with two parallel bases bounded by congruent hexagons and with lateral faces bounded by parallelograms that connect corresponding sides of the bases. The height h of the prism is any perpendicular segment drawn from a point on the base to the plane containing the other base. If the segments that join corresponding vertices of the bases are perpendicular to the bases, then the prism is a right hexagonal prism. Otherwise, it is called oblique. The perimeter formula of a right regular hexagonal prism is P = 12s + 6h where s = side and h = height