Study the pattern. The figures are made up of black squares.
- How many black squares will there be in Figure 8?
- How many black squares will there be in Figure 39?
- Which figure is made up of 2597 black squares?
(a)
Pattern for the number of black squares
Figure
1: 1 x
5 = 1 x (
1 +
4) = 5
Figure
2: 2 x
6 = 2 x (
2 +
4) = 12
Figure
3: 3 x
7 = 3 x (
3 +
4) = 21
Formula
Number of black squares = Figure Number x (Figure Number + 4)
Number of black squares for Figure 8
= 8 x (8 + 4)
= 8 x 12
= 96
(b)
Number of black squares in Figure 39
= 39 x (39 + 4)
= 39 x 43
= 1677
(c)
Figure Number x (Figure Number + 4) = Number of black squares
By guess and check:
Figure Number = 49
49 x 53 = 2597 (✔)
49 x (49 + 4) = 2597
Figure Number with 2597 black squares = 49
Answer(s): (a) 96; (b) 1677; (c) 49
