The diagrams show a pattern made up of squares.
- How many squares are there in Pattern 5?
- How many sides are there in Pattern 5?
- What is the Pattern Number for 378 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 5
= 5 x 6
= 30
(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 5
= 6 + 5 x 12
= 6 + 60
= 66
(c)
6 + Pattern Number x 12 = 378
Pattern Number x 12 = 378 - 6
Pattern Number x 12 = 372
Pattern Number = 372 ÷ 12
Pattern Number = 31
Answer(s): (a) 30; (b) 66; (c) 31