Question

Verify Euler,s relation for pyramid whose base is a polygon of n-side.

Answer 1

Euler's formula:

V - E + F = 2. Let V, F, and E denote the respective number of vertices, faces, and edges of a polyhedron

Consider the situation where our pyramid has an n-sided base.
There are n + 1 faces (the base plus the n triangular faces), there are
2n edges—n around the base and n more connecting the base to the tip, and there are n + 1 vertices—n
around the base plus the tip. Thus F = n + 1, E = 2n and V = n + 1. Euler’s theorem continues to
hold:
F − E + V = (n + 1) − 2n + (n + 1) = 2.(proved)