Study the pattern. Each figure is made up of identical squares.
- What fraction of Figure 1 is shaded? Express your answer in the simplest form.
- What is the number of shaded squares in Figure 4?
- What is the number of unshaded squares in Figure 9?
Figure number |
Total number of squares |
Number of shaded squares |
1 |
4 x 4 = 16 |
1 x 2 + 4 = 6 |
2 |
6 x 6 = 36 |
2 x 2 + 4 = 8 |
3 |
8 x 8 = 64 |
3 x 2 + 4 = 10 |
(a)
Fraction of Figure 1 that is shaded
=
616=
38(b)
Number of shaded squares
Figure 1: 1 x 2 + 4 = 6
Figure 2: 2 x 2 + 4 = 8
Figure 3: 3 x 2 + 4 = 10
Formula:
Number of shaded squares = Figure number x 2 + 4
Number of shaded squares for Figure 4
= 4 x 2 + 4
= 12
(c)
Total number of squares
Figure 1: 4 x 4 = (1 x 2 + 2)2 Figure 2: 6 x 6 = (2 x 2 + 2)2 Figure 3: 8 x 8 = (3 x 2 + 2)2
Formula:
Total number of square tiles = (Figure number x 2 + 2)2
Total number of square tiles for Figure 9
= (9 x 2 + 2)
2 = 20 x 20
= 400
Number of shaded squares in Figure 9
= 9 x 2 + 4
= 22
Number of unshaded squares in Figure 9
= 400 - 22
= 378
Answer(s): (a)
38; (b) 12; (c) 378