Question

3. A polyhedron has 5 faces and 9 edges. Find its number of vertices,​

Answer 1

Answer:

There are 6 vertices in this polyhedron according to Euler's rule.

Step-by-step explanation:

Euler's rule:

F + V - E = 2

5 + V - 9 = 2

V - 4 = 2

V = 2 + 4 = 6

⇒ V = 6

Answer 2

Given:

The number of faces of the polyhedron=5

The number of edges of the polyhedron=9

To find:

The number of vertices

Solution:

The number of vertices is 6.

We can find the number of vertices by following the given steps-

We know that the number of vertices can be calculated using the formula given below-

Number of vertices+Number of faces=2+number of edges

Now, we have the number of faces and edges on the polyhedron.

The number of faces=5

The number of edges=9

Let the number of vertices be V.

On using the above values,

V+5=2+9

V+5=11

V=11-5

V=6

The polyhedron has 6 vertices.

Therefore, the number of vertices is 6.