A pattern is made by Ivan putting shaded squares of unit length around a white square of similar unit length. He then continues to make patterns as shown in Figure 2 and Figure 3.

1. Which figure uses 49 white squares?
2. Find the number of shaded squares in Figure 34.
3. Find the total number of squares in Figure 51.

Pattern
Figure	1	2	3	(a) ?	34	51
Number of white squares	1	4	9	49
Number of shaded squares	8	12	16		(b) ?
Total number of squares	9	16	25			(c) ?

(a)
Pattern for the number of white squares
Figure 1: 1² = 1 x 1 = 1
Figure 2: 2² = 2 x 2 = 4
Figure 3: 3² = 3 x 3 = 9
Figure 4: 4² = 4 x 4 = 16

Number of white squares
= Figure number x Figure number
= Figure number²

Figure number that uses 49 white squares
= √49
= 7

(b)
Patterns for the number of shaded squares
Figure 1: 1 x 4 + 4 = 8
Figure 2: 2 x 4 + 4 = 12
Figure 3: 3 x 4 + 4 = 16

Formula:
Number of shaded squares = Figure Number x 4 + 4

Number of shaded squares in Figure 30
= 34 x 4 + 4
= 140

(c)
Pattern for the total number of squares
Figure 1: (1 + 2)² = 9
Figure 2: (2 + 2)² = 16
Figure 3: (3 + 2)² = 25

Total number of squares = (Figure number + 2)²

Total number of squares for Figure 51
= (51 + 2)²
= 53 x 53
= 2809

Answer(s): (a) 7; (b) 140; (c) 2809