Question

using eulers formula, how many faces does a polyhedron with 14 vertices and 21 edges have? faces

Explanation:

Step1: Recall Euler's formula

Euler's formula for polyhedra is \(V - E+F = 2\), where \(V\) is the number of vertices, \(E\) is the number of edges, and \(F\) is the number of faces.

Step2: Substitute the given values

We are given \(V = 14\) and \(E=21\). Substitute these into the formula: \(14-21 + F=2\).

Step3: Solve for \(F\)

First, simplify the left - hand side of the equation: \(14-21=-7\). So the equation becomes \(-7 + F=2\).
Then, add 7 to both sides of the equation: \(F=2 + 7\).

Answer:

\(9\)