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 10.
- Find the number of shaded squares for Figure 10.
(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 4 is an even-numbered figure.
(iii)
Total number of squares in Figure 4
= (4 + 1)
2 = 5
2 = 5 x 5
= 25
25 ÷ 2 = 12 r 1
(i)
Number of unshaded squares in Figure 4
= 12 + 1
= 13
(ii)
Number of shaded squares in Figure 4 = 12
(b)
Total number of squares in Figure 10
= (10 + 1)
2 = 11
2 = 11 x 11
= 121
121 ÷ 2 = 60 r 1
Number of unshaded squares for Figure 10
= 60 + 1
= 61
(c)
Number of shaded squares for Figure 10 = 60
Answer(s): (a) 13, 12, 25; (b) 61; (c) 60