Question

Verify Euler's formula for pentagonal prism.

Answer 1

For any polyhedron, Number of Faces + Number of Vertices - Number of Edges = 2. This is Euler's formula.
In a Pentagonal Prism,
Number of Faces = 7 (1 is at top, 1 is at bottom and 5 are lateral)
Number of Vertices = 10 (5 are at the top and 5 are at the bottom)
Number of Edges = 15 (5 are at the top, 5 are on the lateral sides and 5 are at the bottom)
So, F + V - E = 2
∴ 7 + 10 - 15
17 - 15
= 2
Hence verified. 

Answer 2

f+V-E=2

=7+10-15

=17-15

=2

pentagonal prism Euler's formula