Question

Given a polyhedron with 6 vertices and 12 edges, how many faces does it have?

Answer 1

GIVEN

A polyhedron has 6 vertices and 12 edges.

TO DETERMINE

The number of faces

CONCEPT TO BE IMPLEMENTED

Euler’s formula for Polyhedron :

For polyhedron F + V = E + 2

Where F stands for number of faces , V stands for number of vertices , E stands for number of edges .

EVALUATION

Here it is given that a polyhedron has 6 vertices and 12 edges

V = Number of vertices = 6

E = Number of edges = 12

F = Number of faces = ?

By Euler’s formula

F + V = E + 2

⇒ F + 6 = 12 + 2

⇒ F + 6 = 14

⇒ F = 8

FINAL ANSWER

The number of faces = 8