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 31.
- Find the perimeter of Figure 51.
(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 31
= 31 x (31 + 1) ÷ 2
= 31 x 32 ÷ 2
= 992 ÷ 2
= 496
Area of a square = 4 x 4 = 16 cm
2 Area of Pattern 31
= 496 x 16
= 7936 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 51
= 51 x (4 x 4)
= 51 x 16
= 816 cm
Answer(s): (a) 231; (b) 7936 cm
2; (c) 816 cm