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

Answer 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

`V-E+F=2\\\\\Rightarrow 20-E+20=2\\\\\Rightarrow 40-E=2\\\\\Rightarrow E=40-2\\\\\Rightarrow E=38.`.

Thus, the required number of edges of the given polyhedron is 38.

Option (C) is CORRECT.