# Answer to Question #2794 in Geometry for Drew Collier

Question #2794

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

Expert's answer

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.

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.

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