An octahedron is a an are figure through 8 faces that are polygons. In the figure below are 3 different species of octahedrons. The prefix "octa" method eight.

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An octahedron deserve to be developed by 2 pyramids v bases in the shape of a quadrilateral, as shown in the figure below.

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Properties of a continual octahedron

A regular octahedron is an octahedron whose faces are every congruent, continual polygons. Otherwise, it is irregular. Regular octahedrons room studied more often.

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A regular octahedron, such as the one shown above, is just one of the 5 Platonic solids, which are a type of consistent polyhedron. A regular octahedron has actually 8 congruent encounters that space congruent it is intended triangles, 12 congruent edges, and also 6 vertices; an edge is a line segment created by the intersection that two adjacent faces; a vertex for a regular octahedron is a allude where 4 edge meet.

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Surface area that a continuous octahedron

We can find the area of among the faces and also multiply it by eight to discover the complete surface area that a continual octahedron. An it is intended triangle v side length, e (also the size of the edges of a constant octahedron), has an area, A, of

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The full surface area, S, the a continual octahedron in terms of its edges, e, is,

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Volume of a consistent octahedron

The volume, V, the a consistent octahedron is

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where e is the size of the edge.


Example:

If the complete surface area that a continuous octahedron is

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, what is its volume?

We can discover e through substituting the provided value in for the full surface area come get