Question

Using Euler's formula, howmany edges does a polyhedronwith 7 faces and 10 verticeshave?[?] edgesEuler's Formula: F + V = E + 2

Answer 1

Given: The following

`\begin{gathered} N_{umber\text{ of faces}}=7 \\ N_{umber\text{ of vertices}}=10 \end{gathered}`

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

`\begin{gathered} F=7 \\ V=10 \\ E=? \end{gathered}`
`\begin{gathered} F+V=E+2 \\ E=F+V-2 \\ E=7+10-2 \\ E=17-2 \\ E=15 \end{gathered}`

Hence, the number of edges possessed by the polyhedron is 15