The diagrams show a pattern made up of squares.
- How many squares are there in Pattern 8?
- How many sides are there in Pattern 8?
- What is the Pattern Number for 546 sides?
(a)
Number of squares:
Pattern 1: 6 = 1 x 6
Pattern 2: 12 = 2 x 6
Pattern 3: 18 = 3 x 6
Formula:
Number of squares = Pattern number x 6
Number of squares in Pattern 8
= 8 x 6
= 48
(b)
Number of sides:
Pattern 1: 18 = 6 + 1 x 12
Pattern 2: 30 = 6 + 2 x 12
Pattern 3: 42 = 6 + 3 x 12
Formula:
Number of sides = 6 + Pattern number x 12
Number of sides in Pattern 8
= 6 + 8 x 12
= 6 + 96
= 102
(c)
6 + Pattern Number x 12 = 546
Pattern Number x 12 = 546 - 6
Pattern Number x 12 = 540
Pattern Number = 540 ÷ 12
Pattern Number = 45
Answer(s): (a) 48; (b) 102; (c) 45
