Question

What are regular polyhedrons? Give a few examples. Can we have general formula for finding their surface areas?

Answer 1

Please see below.

Explanation:

A regular polyhedron is one whose all surfaces are regular polygon. The latter is one whose all sides and interior angles are equal.

Two such well known polyhedrons are tetrahedron (formed by four equal equilateral triangles ) and cube (formed by six equal squares ).

Others are octahedron (formed by eight equal equilateral triangles ), dodechedron (formed by twelve equal regular pentagons ) and icosahedron (formed by twenty equal equilateral triangles ).

These appear as shown below:

Formulas can be generated for finding their surface areas based on either the length of the side of the regular polygon say `a` or the radius of circumscribing circle `R` or radius of inscribing circle `r`. These are based on normal geometric methods including Pythagoras formula and difficult to generalize. The formulas can be found here.