Squares of sides 3 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 30.
- Find the area of Figure 22.
- Find the perimeter of Figure 55.
(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 30
= 30 x (30 + 1) ÷ 2
= (30 x 31) ÷ 2
= 465
(b)
Number of squares for Pattern 22
= 22 x (22 + 1) ÷ 2
= 22 x 23 ÷ 2
= 506 ÷ 2
= 253
Area of a square = 3 x 3 = 9 cm
2 Area of Pattern 22
= 253 x 9
= 2277 cm
2 (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 55
= 55 x (4 x 3)
= 55 x 12
= 660 cm
Answer(s): (a) 465; (b) 2277 cm
2; (c) 660 cm