Study the pattern. Each figure is made up of identical squares.

1. What fraction of Figure 2 is shaded? Express your answer in the simplest form.
2. What is the number of shaded squares in Figure 5?
3. What is the number of unshaded squares in Figure 7?

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 2 that is shaded
= ⁸₃₆
= ²₉

(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 5
= 5 x 2 + 4
= 14

(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 7
= (7 x 2 + 2)²
= 16 x 16
= 256

Number of shaded squares in Figure 7
= 7 x 2 + 4
= 18

Number of unshaded squares in Figure 7
= 256 - 18
= 238

Answer(s): (a) ²₉; (b) 14; (c) 238