Study the pattern. The figures are made up of black squares.
- How many black squares will there be in Figure 10?
- How many black squares will there be in Figure 20?
- Which figure is made up of 725 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 10
= 10 x (10 + 4)
= 10 x 14
= 140
(b)
Number of black squares in Figure 20
= 20 x (20 + 4)
= 20 x 24
= 480
(c)
Figure Number x (Figure Number + 4) = Number of black squares
By guess and check:
Figure Number = 25
25 x 29 = 725 (✔)
25 x (25 + 4) = 725
Figure Number with 725 black squares = 25
Answer(s): (a) 140; (b) 480; (c) 25