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 11.
2. What is the perimeter of Figure 82?
3. Which figure requires a total number of 1855 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 11
= 11 x 8 + 7
= 95

(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 82
= 82 x 2 + 7
= 171

(c)
Figure number x 8 + 7 = 1855
Figure number x 8 = 1855 - 7 = 1848
Figure number = 1848 ÷ 8 = 231

Answer(s): (a) 95; (b) 171; (c) 231