Squares of sides 5 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 22.
- Find the area of Figure 18.
- Find the perimeter of Figure 42.
(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 18
= 18 x (18 + 1) ÷ 2
= 18 x 19 ÷ 2
= 342 ÷ 2
= 171
Area of a square = 5 x 5 = 25 cm
2 Area of Pattern 18
= 171 x 25
= 4275 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 42
= 42 x (4 x 5)
= 42 x 20
= 840 cm
Answer(s): (a) 253; (b) 4275 cm
2; (c) 840 cm