Question

Write Euler’s formula and use it to find the unknown.


FACES VERTICES EDGES

i) ? 4 6

ii) 12 18 ?

iii) 10 ? 22

Answer 1

Answer:

Euler's Formula

F + V = E + 2

F = FACES

V = VERTICES

E = EDGES

1. F + 4 = 6 + 2

F + 4 = 8

F = 8 - 4

F = 4

2. 12 + 18 = E + 2

30 = E + 2

30 - 2 = E

E = 28

3. 10 + V = 22 + 2

10 + V = 24

V = 24 - 10

V = 14

Answer 2

Euler's Formula

F+V=E+2

• i) ? 4 6
• x+4=6+2
• x=8-4
• x=4
• ii) 12 18 ?
• 12+18=x+2
• 30=x+2
• 30-2=x
• x=28

• iii) 10 ? 22
• 10+x=22+2
• 10+x=24
• x=24-10
• x=14