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 36.
- Find the number of shaded squares for Figure 36.
(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 8 is an even-numbered figure.
(iii)
Total number of squares in Figure 8
= (8 + 1)
2 = 9
2 = 9 x 9
= 81
81 ÷ 2 = 40 r 1
(i)
Number of unshaded squares in Figure 8
= 40 + 1
= 41
(ii)
Number of shaded squares in Figure 8 = 40
(b)
Total number of squares in Figure 36
= (36 + 1)
2 = 37
2 = 37 x 37
= 1369
1369 ÷ 2 = 684 r 1
Number of unshaded squares for Figure 36
= 684 + 1
= 685
(c)
Number of shaded squares for Figure 36 = 684
Answer(s): (a) 41, 40, 81; (b) 685; (c) 684