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# Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

**Solution:**

We have to determine which of the given solids are polyhedron by using Euler’s formula.

Euler’s formula for any polyhedron is given by

F + V – E = 2

Where F stands for number of faces,

V for number of vertices

E for number of edges.

From the figure,

Faces = 5, Vertices = 6, and Edges = 9.

Now, F + V - E = 5 + 6 − 9

= 11 - 9

= 2

Therefore, it is a polyhedron.

From the figure,

Faces = 6, Vertices = 8, and Edges = 12

Now, F + V - E = 6 + 8 − 12

= 14 - 12

= 2

Therefore, it is a polyhedron.

From the figure,

Faces = 3, Vertices = 0, and Edges = 2

Now, F + V - E = 3 + 0 − 2

= 3 - 2

= 1

Therefore, it is not a polyhedron.

From the figure,

Faces = 7, Vertices = 10, and Edges = 15

Now, F + V - E = 7 + 10 − 15

= 17 - 15

= 2

Therefore, it is a polyhedron.

**✦ Try This: **Can a polyhedron have F = V = 9 and E = 16.

**☛ Also Check: ** NCERT Solutions for Class 8 Maths Chapter 10

**NCERT Exemplar Class 8 Maths Chapter 6 Problem 67 (a)**

## Look at the shapes given below and state which of these are polyhedra using Euler’s formula.

**Summary:**

Each of the given shapes are verified using Euler’s formula and the polyhedra are mentioned above.

**☛ Related Questions:**

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