Using Euler's formula, howmany edges does a polyhedronwith 7 faces and 10 verticeshave?[?] edgesEuler's Formula: F + V = E + 2
![Using Euler's formula, howmany edges does a polyhedronwith 7 faces and 10 verticeshave?[?] edgesEuler's Formula: F + V = E + 2 class=](https://us-static.z-dn.net/files/dcc/399c0ec6b542dccdd8de62a41548c3ab.png)
Given: The following
[tex]\begin{gathered} N_{umber\text{ of faces}}=7 \\ N_{umber\text{ of vertices}}=10 \end{gathered}[/tex]To Determine: The number of edges
Solution:
The Euler's formula is given as
F + V = E + 2,
where F is the number of faces,
V the number of vertices, and
E the number of edges.
Substitute the given into the formula
[tex]\begin{gathered} F=7 \\ V=10 \\ E=? \end{gathered}[/tex][tex]\begin{gathered} F+V=E+2 \\ E=F+V-2 \\ E=7+10-2 \\ E=17-2 \\ E=15 \end{gathered}[/tex]Hence, the number of edges possessed by the polyhedron is 15