Squares of sides 4 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 21.
- Find the area of Figure 37.
- Find the perimeter of Figure 36.
(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 21
= 21 x (21 + 1) ÷ 2
= (21 x 22) ÷ 2
= 231
(b)
Number of squares for Pattern 37
= 37 x (37 + 1) ÷ 2
= 37 x 38 ÷ 2
= 1406 ÷ 2
= 703
Area of a square = 4 x 4 = 16 cm
2 Area of Pattern 37
= 703 x 16
= 11248 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 36
= 36 x (4 x 4)
= 36 x 16
= 576 cm
Answer(s): (a) 231; (b) 11248 cm
2; (c) 576 cm