Read the pattern and complete the table.
- Find the number of circles in Figure 12.
- Find the figure number that would require a total number of 133 rectangles and circles altogether.
(a)
Pattern for the number of rectangles
Figure 1: 1 rectangle
Figure 2: 2 rectangles
Figure 3: 3 rectangles
Formula:
Number of rectangles = Figure number
Pattern for the number of circles
Figure 1: 1 + 1 x 3 = 4 circles
Figure 2 : 1 + 2 x 3 = 7 circles
Figure 3: 1 + 3 x 3 = 10 circles
Formula:
Number of circles = 1 + Figure number x 3
Number of circles in Figure 12
= 1 + 12 x 3
= 37
(b)
Pattern for the total number of circles and rectangles
Figure 1: 1 + 1 x 4 = 5
Figure 2: 1 + 2 x 4 = 9
Figure 3: 1 + 3 x 4 = 13
Formula:
Total number of rectangles and circles = 1 + Figure number x 4
1 + Figure number x 4 = 133
Figure number x 4 = 133 - 1 = 132
Figure number = 132 ÷ 4 = 33
Answer(s): (a) 37; (b) 33