Squares of sides 3 cm are arranged to create a pattern as shown.

1. Find the number of squares needed for Figure 26.
2. Find the area of Figure 13.
3. Find the perimeter of Figure 52.

(a)
Pattern for the number of squares
Pattern 1: 1
Pattern 2: 1 + 2 = 3
Pattern 3: 1 + 2 + 3 = 6
Pattern 4: 1 + 2 + 3 + 4 = 10

Formula:
Number of squares = Pattern number x (Pattern number +1) ÷ 2

Number of squares for Pattern 26
= 26 x (26 + 1) ÷ 2
= (26 x 27) ÷ 2
= 351

(b)
Number of squares for Pattern 13
= 13 x (13 + 1) ÷ 2
= 13 x 14 ÷ 2
= 182 ÷ 2
= 91

Area of a square = 3 x 3 = 9 cm²

Area of Pattern 13
= 91 x 9
= 819 cm²

(c)
Pattern for the perimeter in cm
Pattern 1: 1 x (4 x 3) = 12
Pattern 2: 2 x (4 x 3) = 24
Pattern 3: 3 x (4 x 3) = 54 
Pattern 4: 4 x (4 x 3) = 48 

Formula:
Perimeter of the pattern = Pattern number x (4 x side length)

Perimeter of Pattern 52
= 52 x (4 x 3)
= 52 x 12
= 624 cm

Answer(s): (a) 351; (b) 819 cm²; (c) 624 cm