Study the pattern. The figures are made up of black squares.
- How many black squares will there be in Figure 11?
- How many black squares will there be in Figure 32?
- Which figure is made up of 1085 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 11
= 11 x (11 + 4)
= 11 x 15
= 165
(b)
Number of black squares in Figure 32
= 32 x (32 + 4)
= 32 x 36
= 1152
(c)
Figure Number x (Figure Number + 4) = Number of black squares
By guess and check:
Figure Number = 31
31 x 35 = 1085 (✔)
31 x (31 + 4) = 1085
Figure Number with 1085 black squares = 31
Answer(s): (a) 165; (b) 1152; (c) 31
