Study the pattern. The figures are made up of black squares.
- How many black squares will there be in Figure 5?
- How many black squares will there be in Figure 32?
- Which figure is made up of 285 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 5
= 5 x (5 + 4)
= 5 x 9
= 45
(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 = 15
15 x 19 = 285 (✔)
15 x (15 + 4) = 285
Figure Number with 285 black squares = 15
Answer(s): (a) 45; (b) 1152; (c) 15