Squares of sides 2 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 34.
- Find the area of Figure 9.
- Find the perimeter of Figure 29.
(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 34
= 34 x (34 + 1) ÷ 2
= (34 x 35) ÷ 2
= 595
(b)
Number of squares for Pattern 9
= 9 x (9 + 1) ÷ 2
= 9 x 10 ÷ 2
= 90 ÷ 2
= 45
Area of a square = 2 x 2 = 4 cm
2 Area of Pattern 9
= 45 x 4
= 180 cm
2 (c)
Pattern for the perimeter in cm
Pattern 1: 1 x (4 x 2) = 8
Pattern 2: 2 x (4 x 2) = 16
Pattern 3: 3 x (4 x 2) = 24
Pattern 4: 4 x (4 x 2) = 32
Formula:
Perimeter of the pattern = Pattern number x (4 x side length)
Perimeter of Pattern 29
= 29 x (4 x 2)
= 29 x 8
= 232 cm
Answer(s): (a) 595; (b) 180 cm
2; (c) 232 cm