Question

a polyhedron has 7 faces and 15 edges how many vertices does this polyhedron have? can you give a special name to this polyhedron ?​

Answer 1

Answer:

According to Euler's formula for polyhedrons

F + V = E + 2

7 + V = 15 + 2

7 + V = 17

V = 17 - 7 = 10

the special name to this polyhedron is pentagonal prism

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Answer 2

The polyhedron has 10 vertices and its special name is 'pentagonal prism'.

Given : The polyhedron has 7 faces and 15 edges.

To find :

1. The number of vertices.
2. The special name for the polyhedron.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of vertices and giving a special name for the polyhedron)

Now, we know that :

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

By, putting the given data, we get :

7 + Number of vertices - 15 = 2

Number of vertices = 2 - 7 + 15

Number of vertices = 10

Now, the polyhedron has

• 7 faces
• 15 edges
• 10 vertices

And, a pentagonal prism also has 7 faces, 15 edges and 10 vertices.

So, the special name will be 'pentagonal prism'.

Hence, the polyhedron has 10 vertices and its special name is 'pentagonal prism'.