Verify the ‘Euler’s formula’ V + F = E + 2 for the given figures.

(a) A triangular prism having 5 faces, 9 edges and 6 vertices.

(b) A rectangular prism with 6 faces, 12 edges and 8 vertices.

(c) A pentagonal prism with 7 faces, 15 edges and 10 vertices.

(d) A tetrahedron -with 4 faces, 6 edges and 4 vertices.

(a) Here, F = 5, E = 9 and V = 6

∴ V + F = E + 2 

⇒ 6 + 5 = 9 + 2 

⇒ 11 = 11

Hence, verified.

(b) Here, F = 6, E = 12 and V = 8

∴ V + F = E + 2

⇒ 8 + 6 = 12 + 2

⇒ 14 = 14

Hence, verified.

(c) Here, F = 7, E = 15 and V = 10

∴ V + F = E + 2

⇒ 10 + 7 = 15 + 2

⇒ 17 = 17

Hence, verified.

(d) Here, F = 4, E = 6 and V = 4

∴ V + F = E + 2

⇒ 4 + 4 = 6 + 2

⇒ 8 = 8

Hence, verified.