Study the pattern. The figures are made up of black squares.
- How many black squares will there be in Figure 12?
- How many black squares will there be in Figure 36?
- Which figure is made up of 2021 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 12
= 12 x (12 + 4)
= 12 x 16
= 192
(b)
Number of black squares in Figure 36
= 36 x (36 + 4)
= 36 x 40
= 1440
(c)
Figure Number x (Figure Number + 4) = Number of black squares
By guess and check:
Figure Number = 43
43 x 47 = 2021 (✔)
43 x (43 + 4) = 2021
Figure Number with 2021 black squares = 43
Answer(s): (a) 192; (b) 1440; (c) 43
