Answer :

Given that (i) face = 7, vertices = 10, edge = x

By using Euler’s formula


We know that


Face + vertices = edge + 2


7 + 10 = x + 2


17 = x + 2


X = 17-2


X = 15.


Given that (ii) face = y, vertices = 12, edge = 18


By using Euler’s formula


We know that


Face + vertices = edge + 2


y + 12 = 18 + 2


y + 12 = 20


y = 20-12


y = 8


Given that (iii) face = 9, vertices = z, edge = 16


By using Euler’s formula


We know that


Face + vertices = edge + 2


9 + z = 16 + 2


9 + z = 18


Z = 18-9


Z = 9.


Given that (iv) face = p, vertices = 6, edge = 12


By using Euler’s formula


We know that


Face + vertices = edge + 2


P + 6 = 12 + 2


P + 6 = 14


P = 14-6


P = 12.


Given that (v) face = 6, vertices = q, edge = 12


By using Euler’s formula


We know that


Face + vertices = edge + 2


6 + q = 12 + 2


6 + q = 14


q = 14-6


q = 8


Given that (vi) face = 8, vertices = 11,edge = r


By using Euler’s formula


We know that


Face + vertices = edge + 2


8 + 11 = r + 2


19 = r + 2


r = 19-2


r = 17


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