Question

Using Euler's formula, find the unknown. [4 MARKS]

$\begin{array}{cccc}\text{Faces}& ?& 5& 20\\ \text{Vertices}& 6& ?& 12\\ \text{Edges}& 12& 9& ?\end{array}$

Answer 1

Formula: 1 Mark
Application: 1 Mark each

Euler's formula = F + V - E = 2

$\Rightarrow$ F + 6 - 12 = 2

F - 6 = 2

F = 8


$\Rightarrow$ 5 + V - 9 = 2

V - 4 = 2

V = 6


$\Rightarrow$ 20 + 12 - E = 2

32 - 2 = E

E = 30