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 26.
- Find the perimeter of Figure 59.
(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 26
= 26 x (26 + 1) ÷ 2
= 26 x 27 ÷ 2
= 702 ÷ 2
= 351
Area of a square = 2 x 2 = 4 cm
2 Area of Pattern 26
= 351 x 4
= 1404 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 59
= 59 x (4 x 2)
= 59 x 8
= 472 cm
Answer(s): (a) 276; (b) 1404 cm
2; (c) 472 cm