Cole formed some figures using squares and circles as shown.
- Find the number of squares in Figure 8.
- Find the total number of circles and squares in Figure 24.
- A figure in the pattern has a total of 4291 circles and squares. What is the Figure Number?
(a)
Number of squares
Figure 1: 2 = 1 + 1
Figure 2: 3 = 1 + 2
Figure 3: 4 = 1 + 3
Figure 4: 5 = 1 + 4
Formula:
Number of squares = 1 + Figure Number
Number of squares in Figure 8
= 1 + 8
= 9
(b)
Total number of circles and squares
Figure 1: 3 = 1 + 2(1)
Figure 2: 7 = 1 + 2(1 + 2)
Figure 3: 13 = 1 + 2(1 + 2 + 3)
Figure 4: 21 = 1 + 2(1 + 2 + 3 + 4)
Formula:
Number of circles and squares= 1 + 2[
12 x Figure Number x (Figure Number + 1)]
Total number of circles and squares
= 1 + 2[
12 x Figure Number x (Figure Number + 1)]
= 1 + 2(
12 x 24 x 25)
= 1 + 24 x 25
= 1 + 600
= 601
(c)
1 + 2[
12 x Figure Number x (Figure Number + 1)] = 4291
2[
12 x Figure Number x (Figure Number + 1)] = 4291 - 1
Figure Number x (Figure Number + 1) = 4290
65 x 66 = 4290
Figure number that has a total number of circles and squares = 65
Answer(s): (a) 9; (b) 601; (c) 65