The following pattern is made up of shaded and unshaded squares.
- Find the values of (i), (ii) and (iii). Give your answers in the following format. (Eg 1, 2, 3)
- Find the number of unshaded squares for Figure 37.
- Find the number of shaded squares for Figure 37.
(a)
Total number of squares:
Figure 1: 4 = 2 x 2 = (1 + 1)
2Figure 2: 9 = 3 x 3 = (2 + 1)
2Figure 3: 16 = 4 x 4 = (3 + 1)
2Figure 4: 25 = 5 x 5 = (4 + 1)
2
Formula:
Total number of squares = (Figure Number + 1)
2
For odd-numbered figures, the number of
unshaded squares is equal to the number of shaded squares.
For even-number figures, the number of
unshaded squares is 1 more than the number of shaded squares.
Figure 9 is an odd-numbered figure.
(iii)
Total number of squares in Figure 9
= (9 + 1)
2 = 10
2 = 10 x 10
= 100
100 ÷ 2 = 50 r 0
(i)
Number of unshaded squares in Figure 9 = 50
(ii)
Number of shaded squares in Figure 9 = 50
(b)
Total number of squares in Figure 37
= (37 + 1)
2 = 38
2 = 38 x 38
= 1444
1444 ÷ 2 = 722 r 0
Number of unshaded squares for Figure 37 = 722
(c)
Number of shaded squares for Figure 37 = 722
Answer(s): (a) 50, 50, 100; (b) 722; (c) 722