A T-shaped block consists of 4 squares of 1 cm
2 each and the perimeter is 10 cm. Study the pattern with 1 block arranged to form 2 blocks and 3 blocks respectively.
- Find the perimeter of the pattern that consists of 27 blocks.
- If a pattern has a perimeter of 126 cm, find the number of squares that makes up the pattern.
(a)
Pattern for the perimeter
1 block: 1 x 4 + 6 = 10
2 blocks: 2 x 4 + 6 = 14
3 blocks: 3 x 4 + 6 = 18
Perimeter = Number of blocks x 4 + 6
Perimeter of a pattern that consists 27 blocks
= 27 x 4 + 6
= 114 cm
(b)
Perimeter = Number of blocks x 4 + 6
Number of blocks = (Perimeter - 6) ÷ 4
Number of blocks that makes up a pattern which has a perimeter of 126 cm
= (126 - 6) ÷ 4
= 120 ÷ 4
= 30
Patterns for the number of squares
1 block: 1 x 4 = 4
2 blocks: 2 x 4 = 8
3 blocks: 3 x 4 = 12
Number of squares = Number of blocks x 4
Number of squares for a pattern that consists of 30 blocks
= 30 x 4
= 120
Answer(s): (a) 114 cm; (b) 120