The diagram shows 3 squares, the length of which are 1 cm, 2 cm and 3 cm respectively. Each square is made up of small squares which has a length of 1 cm and alternate squares are coloured grey and white.
- How many small grey squares are needed to create a square of side 22 cm?
- Find the length of the side of a square if 529 small grey and white squares are used to create it.
- Find the number of small white squares when a square of side 37 cm is created?
(a)
Patterns for the number of grey squares for even-numbered length
2 cm: 2 x 2 ÷ 2 = 2
4 cm: 4 x 4 ÷ 2 = 8
6 cm: 6 x 6 ÷ 2 = 18
Formula for number of small grey squares for even-numbered length:
Number of grey squares = Square length² ÷ 2
Number of grey squares to create a square of side 22 cm
= 22 x 22 ÷ 2
= 484 ÷ 2
= 242
(b)
Patterns for the number of grey and white squares
1 cm: 1
2 = 1 x 1 = 1
2 cm: 2
2 = 2 x 2 = 4
3 cm: 3
2 = 3 x 3 = 9
Formula for total number of grey and white squares:
Total number of grey and white squares = Square length
2 Length of the square side when 529 grey and white squares is
= √529
= 23 cm
(c)
Patterns for the number of white squares for odd-numbered length:
1 cm: (1 x 1 - 1) ÷ 2 = 0
3 cm: (3 x 3 - 1)
÷ 2 = 4
5 cm: (5 x 5 - 1) ÷ 2 = 12
Formula for number of white squares for odd-numbered length:
Number of white squares = (Square length
2 - 1) ÷ 2
Number of white squares when a square of side 37 cm is created
= (37
2 - 1) ÷ 2
= (37 x 37 - 1) ÷ 2
= (1369 - 1) ÷ 2
= 1368 ÷ 2
= 684
Answer(s): (a) 242; (b) 23 cm; (c) 684