Study the pattern. The figures are made up of black squares.
- How many black squares will there be in Figure 6?
- How many black squares will there be in Figure 37?
- Which figure is made up of 1152 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 6
= 6 x (6 + 4)
= 6 x 10
= 60
(b)
Number of black squares in Figure 37
= 37 x (37 + 4)
= 37 x 41
= 1517
(c)
Figure Number x (Figure Number + 4) = Number of black squares
By guess and check:
Figure Number = 32
32 x 36 = 1152 (✔)
32 x (32 + 4) = 1152
Figure Number with 1152 black squares = 32
Answer(s): (a) 60; (b) 1517; (c) 32