Squares of sides 5 cm are arranged to create a pattern as shown.
- Find the number of squares needed for Figure 19.
- Find the area of Figure 19.
- Find the perimeter of Figure 25.
(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 19
= 19 x (19 + 1) ÷ 2
= (19 x 20) ÷ 2
= 190
(b)
Number of squares for Pattern 19
= 19 x (19 + 1) ÷ 2
= 19 x 20 ÷ 2
= 380 ÷ 2
= 190
Area of a square = 5 x 5 = 25 cm
2 Area of Pattern 19
= 190 x 25
= 4750 cm
2 (c)
Pattern for the perimeter in cm
Pattern 1: 1 x (4 x 5) = 20
Pattern 2: 2 x (4 x 5) = 40
Pattern 3: 3 x (4 x 5) = 150
Pattern 4: 4 x (4 x 5) = 80
Formula:
Perimeter of the pattern = Pattern number x (4 x side length)
Perimeter of Pattern 25
= 25 x (4 x 5)
= 25 x 20
= 500 cm
Answer(s): (a) 190; (b) 4750 cm
2; (c) 500 cm