Squares of sides 2 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 36.
- Find the area of Figure 25.
- 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 36
= 36 x (36 + 1) ÷ 2
= (36 x 37) ÷ 2
= 666
(b)
Number of squares for Pattern 25
= 25 x (25 + 1) ÷ 2
= 25 x 26 ÷ 2
= 650 ÷ 2
= 325
Area of a square = 2 x 2 = 4 cm
2 Area of Pattern 25
= 325 x 4
= 1300 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 42
= 42 x (4 x 2)
= 42 x 8
= 336 cm
Answer(s): (a) 666; (b) 1300 cm
2; (c) 336 cm