Question

Using Euler's formula, how manyfaces does a polyhedron with20 vertices and 30 edges have?[? ] facesEuler's Formula: F + V = E + 2

Answer 1

The Euler's Formula is given to be:

$F+V=E+2$

where F is the number of faces, V is the number of vertices, and E is the number of edges.

From the question, we have the following parameters:

$\begin{gathered} V=20 \\ E=30 \end{gathered}$

Therefore, the number of faces can be calculated as shown below:

$\begin{gathered} F+20=30+2 \\ F+20=32 \\ F=32-20 \\ F=12 \end{gathered}$

The polyhedron has 12 faces.