Question

guided practice
use eulers formula to find the number of edges in a polyhedron with four triangular faces and four vertices.
a. 3
b. 4
c. 6
d. 5

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: Identify given values

We are given that \( V = 4 \) (vertices) and \( F = 4 \) (triangular faces).

Step3: Substitute into Euler's Formula

Substitute \( V = 4 \) and \( F = 4 \) into \( V - E + F = 2 \):
\[
4 - E + 4 = 2
\]

Step4: Solve for \( E \)

Simplify the left - hand side: \( 8 - E = 2 \).
Subtract 8 from both sides: \( -E = 2 - 8=-6 \).
Multiply both sides by - 1: \( E = 6 \).

Answer:

C. 6