Squares of sides 3 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 18.
- Find the area of Figure 9.
- Find the perimeter of Figure 24.
(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 18
= 18 x (18 + 1) ÷ 2
= (18 x 19) ÷ 2
= 171
(b)
Number of squares for Pattern 9
= 9 x (9 + 1) ÷ 2
= 9 x 10 ÷ 2
= 90 ÷ 2
= 45
Area of a square = 3 x 3 = 9 cm
2 Area of Pattern 9
= 45 x 9
= 405 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 24
= 24 x (4 x 3)
= 24 x 12
= 288 cm
Answer(s): (a) 171; (b) 405 cm
2; (c) 288 cm