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

1. Find the number of squares needed for Figure 25.
2. Find the area of Figure 33.
3. Find the perimeter of Figure 41.

(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 25
= 25 x (25 + 1) ÷ 2
= (25 x 26) ÷ 2
= 325

(b)
Number of squares for Pattern 33
= 33 x (33 + 1) ÷ 2
= 33 x 34 ÷ 2
= 1122 ÷ 2
= 561

Area of a square = 3 x 3 = 9 cm²

Area of Pattern 33
= 561 x 9
= 5049 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 41
= 41 x (4 x 3)
= 41 x 12
= 492 cm

Answer(s): (a) 325; (b) 5049 cm²; (c) 492 cm