Squares of sides 3 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 38.
- Find the area of Figure 37.
- Find the perimeter of Figure 56.
(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 38
= 38 x (38 + 1) ÷ 2
= (38 x 39) ÷ 2
= 741
(b)
Number of squares for Pattern 37
= 37 x (37 + 1) ÷ 2
= 37 x 38 ÷ 2
= 1406 ÷ 2
= 703
Area of a square = 3 x 3 = 9 cm
2 Area of Pattern 37
= 703 x 9
= 6327 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 56
= 56 x (4 x 3)
= 56 x 12
= 672 cm
Answer(s): (a) 741; (b) 6327 cm
2; (c) 672 cm