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 43.
- Find the number of shaded squares for Figure 43.
(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 5 is an odd-numbered figure.
(iii)
Total number of squares in Figure 5
= (5 + 1)
2 = 6
2 = 6 x 6
= 36
36 ÷ 2 = 18 r 0
(i)
Number of unshaded squares in Figure 5 = 18
(ii)
Number of shaded squares in Figure 5 = 18
(b)
Total number of squares in Figure 43
= (43 + 1)
2 = 44
2 = 44 x 44
= 1936
1936 ÷ 2 = 968 r 0
Number of unshaded squares for Figure 43 = 968
(c)
Number of shaded squares for Figure 43 = 968
Answer(s): (a) 18, 18, 36; (b) 968; (c) 968