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 25?
- Which figure is made up of 621 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 25
= 25 x (25 + 4)
= 25 x 29
= 725
(c)
Figure Number x (Figure Number + 4) = Number of black squares
By guess and check:
Figure Number = 23
23 x 27 = 621 (✔)
23 x (23 + 4) = 621
Figure Number with 621 black squares = 23
Answer(s): (a) 45; (b) 725; (c) 23
