Each of the figures is made up of 1-cm matchsticks.
The table shows the number of matchsticks used to make the figures and their perimeters.

1. Find the number of matchsticks in Figure 12.
2. What is the perimeter of Figure 136?
3. Which figure requires a total number of 2991 matchsticks?

(a)
Pattern for the number of matchsticks
Figure 1: 1 x 8 + 7 = 15
Figure 2: 2 x 8 + 7 = 23
Figure 3: 3 x 8 + 7 = 31

Formula:
Number of matchsticks = Pattern number x 8 + 7

Number of matchsticks in Figure 12
= 12 x 8 + 7
= 103

(b)
Pattern for the perimeter of the figure
Figure 1 = 1 x 2 + 7 = 9
Figure 2 = 2 x 2 + 7 = 11
Figure 3 = 3 x 2 + 7 = 13

Formula:
Perimeter of the figure = Pattern number x 2 + 7

Perimeter of figure 136
= 136 x 2 + 7
= 279

(c)
Figure number x 8 + 7 = 2991
Figure number x 8 = 2991 - 7 = 2984
Figure number = 2984 ÷ 8 = 373

Answer(s): (a) 103; (b) 279; (c) 373