Question

verify euler theorem for the following polyhedra
1)cuboid
2) pentagonal prism
3) heptagonal prism
4)triangular pyramid
5)hexagonal pyramid ​

Answer 1

Answer:

in eulars theorem if F+V-E=2 the solid is a poly hedron.

here',f=face

v=vertices

e=edges

Step-by-step explanation:

1.cuboid

f=6

v=8

e=12

putting eulars theoram=6+8-12=2

;therefore it is a polyhedron

.2.pentagonal prism

f-7

v-10

e-15

putting eulars theoram=7+10-15=2

*therefore it is a polyhedron

3.heptagonal prism

f-9

e-21

v-14

putting eulars theoram=9+14-21=2

*therefore it is a polyhedron

4.triangular pyramid

f.-4

v-4

e-6

putting eulers theoram=4+4-6=2

*therefore it is a polyhedron.

5.hexagonal pyramid=

f=7

v=7

e=12

putting eulars ttheoram=7+7-12=2

*therefore it is a polyhedron.