Question

Using Euler's formula, find the values of x, y, z.

	Faces	Vertices	Edges
(i)	x	15	20
(ii)	6	y	8
(iii)	14	26	z

Answer 1

We will solve for x, y, and z using Euler's formula for polyhedra:

V − E + F = 2

Where:

• V = Number of vertices,
• E = Number of edges,
• F = Number of faces.

(i) Find x (Number of Faces)

• V = 15,
• E = 20
• F = x

Using Euler's formula:

15 − 20 + x = 2

−5 + x = 2

x = 7

(ii) Find y (Number of Vertices)

• V = y,
• E = 8
• F = 6

Using Euler's formula:

y − 8 + 6 = 2

y − 2 = 2

y = 4

(iii) Find z (Number of Edges)

Given:

• V = 26,
• E = z
• F = 14

26 − z + 14 = 2

40 − z = 2

z = 38

Final Answers:

• x = 7,
• y = 4
• z = 38