Squares of sides 3 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 22.
- Find the area of Figure 29.
- Find the perimeter of Figure 36.
(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 22
= 22 x (22 + 1) ÷ 2
= (22 x 23) ÷ 2
= 253
(b)
Number of squares for Pattern 29
= 29 x (29 + 1) ÷ 2
= 29 x 30 ÷ 2
= 870 ÷ 2
= 435
Area of a square = 3 x 3 = 9 cm
2 Area of Pattern 29
= 435 x 9
= 3915 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 36
= 36 x (4 x 3)
= 36 x 12
= 432 cm
Answer(s): (a) 253; (b) 3915 cm
2; (c) 432 cm