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