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Explain why is cube a prism?

Updated: 10/17/2024
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Ronaldono1fan

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βˆ™ 14y ago

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From the Prism (geometry) Wiki - In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms.

Taking this and relating it to a cube, the n-sided base is one of the faces of the cube (any will do as they will all be equal in terms of size and internal/external angles) and the translated copy is the opposite face on the cube.

Because the n-sided base has 4 sides, it leads that there are 4 faces connected to this base, which will make up the sides of the cube.

In a cube the length of these 4 side faces will be equal in length to the width and length of the base - this makes the cube different to any other 6 sided prism (aka Rhombohedron).

If the length of the side faces wasn't equal in length to the width and length of the base the resulting shape would still be a prism and a rhombohedron, but it would no longer be a cube.

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