Squares of sides 5 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 30.
- Find the area of Figure 34.
- Find the perimeter of Figure 47.
(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 30
= 30 x (30 + 1) ÷ 2
= (30 x 31) ÷ 2
= 465
(b)
Number of squares for Pattern 34
= 34 x (34 + 1) ÷ 2
= 34 x 35 ÷ 2
= 1190 ÷ 2
= 595
Area of a square = 5 x 5 = 25 cm
2 Area of Pattern 34
= 595 x 25
= 14875 cm
2 (c)
Pattern for the perimeter in cm
Pattern 1: 1 x (4 x 5) = 20
Pattern 2: 2 x (4 x 5) = 40
Pattern 3: 3 x (4 x 5) = 150
Pattern 4: 4 x (4 x 5) = 80
Formula:
Perimeter of the pattern = Pattern number x (4 x side length)
Perimeter of Pattern 47
= 47 x (4 x 5)
= 47 x 20
= 940 cm
Answer(s): (a) 465; (b) 14875 cm
2; (c) 940 cm