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Verify Euler's formula for the following solids :

1.Hexagonal pyramid

2.Hexagonal prism

3.pentagonal pyramid

4.pentagonal pyramid

Dear student,

Euler's formula = Faces + Vertices - Edges

**Hexagonal**** pyramid**

Faces of a hexagonal pyramid = 7

Vertices of a hexagonal pyramid = 7

Edges of a hexagonal pyramid =12

**Hexagonal prism **

the hexagonal prism is a prism with hexagonal base. This shape has 8 faces, 18 edges, and 12 vertices

**Pentagonal pyramid**

According to Euler’s formulae,

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

In the given pentagonal pyramid,

Number of vertices = 6

Number of faces = 6

Number of edges = 10

Number of vertices + Number of faces – Number of edges = 6 + 6 –10 = 2.

Hence, Euler’s formula is verified.

**Pentagonal Prism**

Euler's formula = Faces + Vertices - Edges = 2

= 7 +7 - 12 = 2

= 14 -12 = 2

Number of faces, F = 6

Number of edges, E = 12

Number of vertices, V = 8

**F + V – E **= 6 + 8 – 12 = 14 – 12 = **2**

Regards

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