Study the pattern. The figures are made up of black squares.
- How many black squares will there be in Figure 7?
- How many black squares will there be in Figure 30?
- Which figure is made up of 957 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 7
= 7 x (7 + 4)
= 7 x 11
= 77
(b)
Number of black squares in Figure 30
= 30 x (30 + 4)
= 30 x 34
= 1020
(c)
Figure Number x (Figure Number + 4) = Number of black squares
By guess and check:
Figure Number = 29
29 x 33 = 957 (✔)
29 x (29 + 4) = 957
Figure Number with 957 black squares = 29
Answer(s): (a) 77; (b) 1020; (c) 29
