Question

What will be the number of edges if there are 12 vertices and 20 faces in a solid​

Answer 1

Answer:

According to the formula given by Euler.

F + V = E + 2

Where,

F = no. of faces

V = no. of vertices

E = no. of edges

So,

F+V=E+2

=> 20 + 12 = E + 2

=> 32 = E + 2

=> E = 32 - 2

=> E = 30

Therefore, there are 30 edges of a polyhedron having 20 faces and 12 vertices.

Answer 2

The number of edges = 30

Given :

There are 12 vertices and 20 faces in a solid

To find :

The number of edges

Concept :

Euler’s formula for Polyhedron :

For polyhedron F + V = E + 2

Where F stands for number of faces , V stands for number of vertices , E stands for number of edges

Solution :

Step 1 of 2 :

Write down number of faces , number of vertices , number of edges

V = Number of vertices = 12

F = Number of faces = 20

E = Number of edges = ?

Step 2 of 2 :

Find number of edges

We use Euler’s formula

By Euler’s formula

F + V = E + 2

⇒ 20 + 12 = E + 2

⇒ E + 2 = 32

⇒ E = 32 - 2

⇒ E = 30

The number of edges = 30

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