Squares of sides 2 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 22.
- Find the area of Figure 8.
- 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 22
= 22 x (22 + 1) ÷ 2
= (22 x 23) ÷ 2
= 253
(b)
Number of squares for Pattern 8
= 8 x (8 + 1) ÷ 2
= 8 x 9 ÷ 2
= 72 ÷ 2
= 36
Area of a square = 2 x 2 = 4 cm
2 Area of Pattern 8
= 36 x 4
= 144 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 24
= 24 x (4 x 2)
= 24 x 8
= 192 cm
Answer(s): (a) 253; (b) 144 cm
2; (c) 192 cm