. polyhedron shapes

Best Answer

A polyhedron is a 3-dimensional solid made of polygons. It has flat faces, straight edges, and vertices. For example, a cube, prism, or pyramid are polyhedrons. Cones, spheres, and cylinders are non-polyhedrons because their sides are not polygons and that they have curved surfaces. The plural of a polyhedron is also called polyhedra. They are categorized as prisms, pyramids, and platonic solids.

Formula to find diagonal of cube

Sol. Diagonal of a cube formula is √3 x units.

Derivation of Diagonal of a Cube Formula

considering the side of the cube as x, a face diagonal as r, and body diagonal as d

By using the Pythagoras theorem

We get, x² + r² = d²

we know that, face diagonal is √2 x

i.e. r = √2

By substituting the value of r in Pythagoras equation we have,

x² + (√2 x )² = d²

x² + 2x² = d²

3x² = d²

d = √3x²

d = √3 x