Study the patterns.

1. Find the total number of triangles in Figure 23.
2. Express the biggest triangle as a percentage of the total possible number of triangles in Figure 23. Correct your answer to 2 decimal places.

(a)
Pattern of the total number of triangles in the figure
Figure 1: 1 x 3 = 3
Figure 2: 2 x 3 = 6
Figure 3: 3 x 3 = 9

Formula:
Total number of triangles in the figure = Figure number x 3 

Total number of triangles in Figure 23
= 23 x 3
= 69 

(b)
Pattern of the biggest triangle as a percentage of the total number of triangles
Figure 1: 1 ÷ 3 x 100% = 33.3%
Figure 2: 1 ÷ 6 x 100% = 16.7%
Figure 3: 1 ÷ 9 x 100% = 11.1%

Formula:
Biggest triangle as a percentage of the total number of triangles = 1 ÷ total number of triangles in the figure x 100%

Biggest triangle as a percentage of the total number of triangles in Figure 23
= 1 ÷ 69 x 100%
= 1.45%

Answer(s): (a) 69; (b) 1.45%