Question

Please solve this its really urgent

Answer 1

we know,
Euler formula:
F+V=E+2
so,
D is not a polyhedron as we can see
in that fig.
f=6
v=10
e=15
so according to euler's formula:
6+10=15+2
16is not equal to17....
therefore d is not a polyhedron
And also c is not a polyhedron

Answer 2

Euler's formula=F+V=E+2
For fig.1:faces=5
Edges=9
Vertices=6
F+v=e+2
5+6=9+2
11=11
therefore,LHS=RHS
fig. a is a polyhedron.

For fig. b,
Faces=5
Edges=12
Vertices=8
F+v=e+2
5+8=12+2
14=14
therefore,fig.b is also a polyhedron.

For fig.c,
Faces=1
Vertices=0
Edges=1
therefore,f+ v=e+2
1+0=1+2
1≠3
therefore fig.c is not a polyhedron.

For fig.d,
Faces=7
Edges=15
Vertices=10
F+v=e+2
7+10=15+2
17=17
therefore fig.d is also a polyhedron.