Squares of sides 2 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 23.
- 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 23
= 23 x (23 + 1) ÷ 2
= (23 x 24) ÷ 2
= 276
(b)
Number of squares for Pattern 31
= 31 x (31 + 1) ÷ 2
= 31 x 32 ÷ 2
= 992 ÷ 2
= 496
Area of a square = 2 x 2 = 4 cm
2 Area of Pattern 31
= 496 x 4
= 1984 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 51
= 51 x (4 x 2)
= 51 x 8
= 408 cm
Answer(s): (a) 276; (b) 1984 cm
2; (c) 408 cm