Study the pattern.
- Find the total number of white and grey triangles in Figure 80.
- Find the percentage of grey triangles in Figure 80.
(a)
Total number of triangles.
Figure 1: 1 = 1 x 1
Figure 2: 4 = 2 x 2
Figure 3: 9 = 3 x 3
Figure 4: 16 = 4 x 4
Figure 5: 25 = 5 x 5
Formula:
Total number of triangles = Figure number x figure number
Total number of grey and white triangles for Figure 80
= 80 x 80
= 6400
(b)
Difference in the number of white and grey triangles.
Figure 1: 1 - 0 = 1
Figure 2: 3 - 1 = 2
Figure 3: 6 - 3 = 3
Figure 4: 10 - 6 = 4
Formula:
Difference in the number of white and grey triangles = Figure number
Number of white triangles = 1 u
Number of grey triangles = 1 u + Figure Number
Total number of triangles
= 80 x 80
= 6400
1 u + 1 u + 80 = 6400
2 u = 6400 - 80
2 u = 6320
1 u = 6320 ÷ 2 = 3160
Number of grey triangles
= 1 u + 80
= 3160 + 80
= 3240
Percentage of grey triangles in Figure 80
=
32406400 x 100%
= 50.625%
Answer(s): (a) 6400; (b) 50.625%