Each figure is made up of a number of identical rods of 1-cm length.

1. Find the perimeter of Figure 45.
2. Find the number of rods in Figure 111.
3. Given that a figure has a perimeter, P, of 418 cm, find the number of squares in this figure.

Figure Number	Number of squares	Number of triangles	Perimeter (P)	Number of rods
1	1	2	6	8
2	2	4	10	15
3	3	6	14	22
4	4	8	18	...
...	...	...	...	...
8	...	...	...	...

(a)
Pattern for perimeter in cm
Figure 1: 1 x 4 + 2 = 6
Figure 2: 2 x 4 + 2 = 10
Figure 3: 3 x 4 + 2 = 14

Perimeter = Figure number x 4 + 2

Perimeter for Figure 45
= 45 x 4 + 2
= 182 cm

(b)
Pattern for the number of rods
Figure 1: 1 x 7 + 1 = 8
Figure 2: 2 x 7 + 1 = 15
Figure 3: 3 x 7 + 1 = 22

Number of rods = Figure number x 7 + 1

Number of rods in Figure 111
= 111 x 7 + 1
= 778

(c)
Perimeter = Figure number x 4 + 2
Figure number = (Perimeter - 2) ÷ 4

Figure number with the perimeter 418 cm
= (418 - 2) ÷ 4
= 416 ÷ 4
= 104

Pattern for the number of squares
Figure 1: 1
Figure 2: 2
Figure 3: 3

Number of squares = Figure number

Number of squares for Figure 104 = 104

Answer(s): (a) 182 cm; (b) 778; (c) 104