The patterns are made up of identical shaded and identical unshaded squares.
- Find the total number of squares in Pattern 7.
- Find the number of unshaded squares in Pattern 7.
- Which Pattern Number has a total of 81 squares?
(a)
Total number of squares:
Pattern 1 = 9 = 3
2 = (1 + 2)2
Pattern 2 = 16 = 4
2 = (2 + 2)
2 Pattern 3 = 25 = 5
2 = (3 + 2)
2 Formula:
Total number of squares = (Pattern Number + 2)
2 Total number of squares in Pattern 7
= (7 + 2)
2 = 9
2
= 9 x 9
= 81
(b)
Number of unshaded squares
= 81 - 4
= 77
(c)
(Pattern Number + 2)
2 = 81
(Pattern Number + 2)
2 = 9 x 9
(Pattern Number + 2)
2 = 9
2 Pattern Number + 2 = 9
Pattern Number = 9 - 2
Pattern Number = 7
Pattern Number that has a total of 81 squares = 7
Answer(s): (a) 81; (b) 77; (c) 7