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

Question

Use Euler’s formula to answer question.

A polyhedrons has 20 vertices and 20 faces. How many edges does it have?

Options are
-42
-40
-38
-39

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1 week 2021-09-09T14:35:58+00:00 1 Answer 0

1. 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 edges of 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 = 20

and

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.