Squares of sides 3 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 36.
- Find the area of Figure 27.
- 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 36
= 36 x (36 + 1) ÷ 2
= (36 x 37) ÷ 2
= 666
(b)
Number of squares for Pattern 27
= 27 x (27 + 1) ÷ 2
= 27 x 28 ÷ 2
= 756 ÷ 2
= 378
Area of a square = 3 x 3 = 9 cm
2 Area of Pattern 27
= 378 x 9
= 3402 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 29
= 29 x (4 x 3)
= 29 x 12
= 348 cm
Answer(s): (a) 666; (b) 3402 cm
2; (c) 348 cm