Study the pattern. The figures are made up of black squares.
- How many black squares will there be in Figure 4?
- How many black squares will there be in Figure 44?
- Which figure is made up of 1292 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 4
= 4 x (4 + 4)
= 4 x 8
= 32
(b)
Number of black squares in Figure 44
= 44 x (44 + 4)
= 44 x 48
= 2112
(c)
Figure Number x (Figure Number + 4) = Number of black squares
By guess and check:
Figure Number = 34
34 x 38 = 1292 (✔)
34 x (34 + 4) = 1292
Figure Number with 1292 black squares = 34
Answer(s): (a) 32; (b) 2112; (c) 34
