Answer to Question #2794 in Geometry for Drew Collier

Question

How do i find the demensions of a regular pyramid if i already have the surface area?

Answer 1

You need to know at least one side of pyramid and the number n of edges in the base.

Its surface is the sum of the area of base and area of its side faces
S = Sbase + Sside

If you know the length& A of the edge in the base, the you can calculate& Sbase
Sbase = n A^2 /4 ctg(/n)

Then you can get& Sside:
Sside =& S - Sbase
&
Further, let Sface the area ofone sice face.
Then
Sside = n * Sface

Every side face is a isosceles triangle with base A.
Then from its area Sface abd the length A of the base you can calculate all its edges.