Michael is making a geometric pattern using sticks to make pentagons.
The first 3 shapes in the pattern are shown below.
- Draw the next shape in the pattern. (1 mark)
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- Complete the table of values using the pattern. (2 marks)
Number of pentagons \((\large p)\) \(\ \ 1\ \ \) \(\ \ 2\ \ \) \(\ \ 3\ \ \) \(\ \ 4\ \ \) Number of sticks \((\large s)\) \(\ \ 5\ \ \) - Write the rule connecting the number of sticks \((s)\) to the number of pentagons \((p)\). (2 marks)
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- How many sticks will be needed to make \(12\) pentagons? (2 marks)
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Show Answers Only
a. \(\text{Shape number }4\)
b. \(\text{Table of values}\)
| \(\text{Number of pentagons }(\large p)\) | \(\ \ 1\ \ \) | \(\ \ 2\ \ \) | \(\ \ 3\ \ \) | \(\ \ 4\ \ \) |
| \(\text{Number of sticks }(\large s)\) | \(\ \ 5\ \ \) | \(\ \ 9\ \ \) | \(\ \ 13\ \ \) | \(\ \ 17\ \ \) |
c. \(s=4\times p+1\)
d. \(49\)
Show Worked Solution
a. \(\text{Shape number }4\)
b. \(\text{Table of values}\)
| \(\text{Number of pentagons }(\large p)\) | \(\ \ 1\ \ \) | \(\ \ 2\ \ \) | \(\ \ 3\ \ \) | \(\ \ 4\ \ \) |
| \(\text{Number of sticks }(\large s)\) | \(\ \ 5\ \ \) | \(\ \ 9\ \ \) | \(\ \ 13\ \ \) | \(\ \ 17\ \ \) |
c. \(\text{Rule: The number of sticks}=4\times \text{(the number of pentagons)}+1\)
\(\therefore\ \text{Rule: }\ s=4\times p+1\)
d. \(\text{Find the value of }s\ \text{when }p=12\)
\(s=4\times p+1=4\times 12+1=49\)