Squares of sides 2 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 32.
- Find the area of Figure 13.
- Find the perimeter of Figure 23.
(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 32
= 32 x (32 + 1) ÷ 2
= (32 x 33) ÷ 2
= 528
(b)
Number of squares for Pattern 13
= 13 x (13 + 1) ÷ 2
= 13 x 14 ÷ 2
= 182 ÷ 2
= 91
Area of a square = 2 x 2 = 4 cm
2 Area of Pattern 13
= 91 x 4
= 364 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 23
= 23 x (4 x 2)
= 23 x 8
= 184 cm
Answer(s): (a) 528; (b) 364 cm
2; (c) 184 cm