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If you know the number of face and vertices a polyhedron has how can you solve for how many edges it has? Example: If a polyhedron has 5 faces and 7 vertices, then it must have how many edges?

Respuesta :

calculista

Answer:

10 edges

Step-by-step explanation:

we know that

The Euler's formula state that: In a polyhedron, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

[tex]V - E + F = 2[/tex]

in this problem  we have

[tex]V=7\\E=?\\F=5[/tex]

substitute the given values

[tex]7 - E + 5 = 2[/tex]

solve for E

Combine like terms in the left side

[tex]12 - E = 2[/tex]

subtract 12 both sides

[tex]- E = -10[/tex]

Multiply by -1 both sides

[tex]E =10[/tex]

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