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Use Euler’s formula to answer question. A polyhedrons has 20 vertices and 20 faces. How many edges does it have?

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## Answers ( )

Answer: The correct option is (C) 38.Step-by-step explanation:Given that a polyhedron has 20 vertices and 20 faces.We are to find the

number of edgesof the polyhedron using Euler’s formula.Euler’s formula :For any polyhedron, the number of vertices and faces together is exactly two more than the number of edges.

Mathematically,

V − E + F = 2,where V, E and F represents the number of vertices, number of edges and number of faces of the polyhedron.For the given polyhedron, we have

number of vertices,

V = 20,number of faces,

F = 20and

number of edges,

E = ?Therefore, from Euler’s formula.

Thus, the required number of edges of the given polyhedron is 38.Option (C) is CORRECT.