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 25 cm?
- Find the length of the side of a square if 324 small grey and white squares are used to create it.
- Find the number of small white squares when a square of side 38 cm is created?
(a)
Patterns for the number of grey squares for odd-numbered length
1 cm: (1 x 1 + 1) ÷ 2 = 1
3 cm: (3 x 3 + 1) ÷ 2 = 5
5 cm: (5 x 5 + 1) ÷ 2 = 13
Formula for number of small grey squares for odd-numbered length:
Number of grey squares = (Square length² + 1) ÷ 2
Number of grey squares to create a square of side 25 cm
= (25 x 25 + 1) ÷ 2
= (625 + 1) ÷ 2
= 313
(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 324 grey and white squares is
= √324
= 18 cm
(c)
Patterns for the number of white 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 white squares for even-numbered length:
Number of white squares = Square length
2 ÷ 2
Number of white squares when a square of side 38 cm is created
= 38
2 ÷ 2
= 38 x 38 ÷ 2
= 1444 ÷ 2
= 722
Answer(s): (a) 313; (b) 18 cm; (c) 722