Squares of sides 4 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 24.
- Find the area of Figure 34.
- Find the perimeter of Figure 39.
(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 24
= 24 x (24 + 1) ÷ 2
= (24 x 25) ÷ 2
= 300
(b)
Number of squares for Pattern 34
= 34 x (34 + 1) ÷ 2
= 34 x 35 ÷ 2
= 1190 ÷ 2
= 595
Area of a square = 4 x 4 = 16 cm
2 Area of Pattern 34
= 595 x 16
= 9520 cm
2 (c)
Pattern for the perimeter in cm
Pattern 1: 1 x (4 x 4) = 16
Pattern 2: 2 x (4 x 4) = 32
Pattern 3: 3 x (4 x 4) = 96
Pattern 4: 4 x (4 x 4) = 64
Formula:
Perimeter of the pattern = Pattern number x (4 x side length)
Perimeter of Pattern 39
= 39 x (4 x 4)
= 39 x 16
= 624 cm
Answer(s): (a) 300; (b) 9520 cm
2; (c) 624 cm