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 40.
- Find the number of shaded squares for Figure 40.
(a)
Total number of squares:
Figure 1: 4 = 2 x 2 = (1 + 1)
2 Figure 2: 9 = 3 x 3 = (2 + 1)
2 Figure 3: 16 = 4 x 4 = (3 + 1)
2
Figure 4: 25 = 5 x 5 = (4 + 1)
2
Formula:
Total number of squares = (Figure Number + 1)
2For 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 6 is an even-numbered figure.
(iii)
Total number of squares in Figure 6
= (6 + 1)
2 = 7
2 = 7 x 7
= 49
49 ÷ 2 = 24 r 1
(i)
Number of unshaded squares in Figure 6
= 24 + 1
= 25
(ii)
Number of shaded squares in Figure 6 = 24
(b)
Total number of squares in Figure 40
= (40 + 1)
2 = 41
2 = 41 x 41
= 1681
1681 ÷ 2 = 840 r 1
Number of unshaded squares for Figure 40
= 840 + 1
= 841
(c)
Number of shaded squares for Figure 40 = 840
Answer(s): (a) 25, 24, 49; (b) 841; (c) 840