Using Euler's formula, find the unknown.

	(i)	(ii)
Faces	x	5
Vertices	6	y
Edges	12	9

 

Euler's Formula: F + V - E = 2

Case(i) Here, F = x, V = 6 and E = 12

Therefore, F + V - E = 2

Or, x + 6 - 12 = 2

Or, x - 6 = 2

Or, x = 2 + 6 = 8

Hence, number of faces are 8.

Case (ii) Here, F = 5, V = y and E = 9

Therefore, F + V - E = 2

Or, 5 + y - 9 = 2

Or, y - 4 = 2

Or, y = 2 + 4 = 6

Hence, number of vertices are 6.