Squares of sides 2 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 33.
- Find the area of Figure 17.
- Find the perimeter of Figure 54.
(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 33
= 33 x (33 + 1) ÷ 2
= (33 x 34) ÷ 2
= 561
(b)
Number of squares for Pattern 17
= 17 x (17 + 1) ÷ 2
= 17 x 18 ÷ 2
= 306 ÷ 2
= 153
Area of a square = 2 x 2 = 4 cm
2 Area of Pattern 17
= 153 x 4
= 612 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 54
= 54 x (4 x 2)
= 54 x 8
= 432 cm
Answer(s): (a) 561; (b) 612 cm
2; (c) 432 cm