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Using Euler's formula, how many edges does a polyhedron with 6 faces and 8 vertices have?

Euler's Formula: [tex]F + V = E + 2[/tex]

[tex]F = 6[/tex]
[tex]V = 8[/tex]
[tex]E = ?[/tex]

How many edges does the polyhedron have?

[?] edges

Sagot :

GinnyAnsweridn
To determine the number of edges [tex]\( E \)[/tex] in a polyhedron with 6 faces ([tex]\( F \)[/tex]) and 8 vertices ([tex]\( V \)[/tex]), we can use Euler's formula for polyhedra. Euler's formula is given by:
[tex]\[ F + V = E + 2 \][/tex]

Here's a step-by-step solution:

1. Identify the given values:
- Number of faces ([tex]\( F \)[/tex]): 6
- Number of vertices ([tex]\( V \)[/tex]): 8

2. Substitute the known values into Euler's formula:
[tex]\[ 6 + 8 = E + 2 \][/tex]

3. Simplify the equation to solve for [tex]\( E \)[/tex]:
[tex]\[ 14 = E + 2 \][/tex]

4. Isolate [tex]\( E \)[/tex] by subtracting 2 from both sides of the equation:
[tex]\[ 14 - 2 = E \][/tex]
[tex]\[ 12 = E \][/tex]

Therefore, the polyhedron has [tex]\( 12 \)[/tex] edges.

So, a polyhedron with 6 faces and 8 vertices has [tex]\(\boxed{12}\)[/tex] edges.
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