paper downloadable from

hereQ29

Figure 1: 4 Nodes 4 Regions 6 Arcs

Figure 2: 6 Nodes 8 Regions 12 Arcs

Figure 3: 2 Nodes 1 Regions 1 Arcs

Figure 4: 7 Nodes 5 Regions 10 Arcs

Arcs = Nodes + Regions -2

Q30

How many diagonals does a hexagon have? 9

How many diagonals does an octagon have? 20

Complete the following table:

Number of sides = 3 Number of diagonals = 0

Number of sides = 4 Number of diagonals = 2

Number of sides = 5 Number of diagonals = 5

Number of sides = 6 Number of diagonals = 9

Number of sides = 7 Number of diagonals = 14

Number of sides = 8 Number of diagonals = 20

Number of sides = n Number of diagonals = (n-3)x(n/2)

Number of sides = 20 Number of diagonals = 170

from each vertex you can draw diagonals to each of the vertices except itself, and the two adjacent to it (which will form the sides of the polygon) - i.e. n(the number of vertices - which is the same as the number of sides) - 3

multiply this by the number of vertices

then divide by two as you would otherwise be counting each diagonal from both its source end and its destination end

hence (n-3)x(n/2)