# Pow 8 Just Count the Pegs

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Just count the Pegs

Freddie Short has a new shortcut to find the area of any polygon on the geoboard that has no pegs on the interior. His formula is like a rule for an In-Out in which the In is the number of pegs on the boundary and out is the area of the figure. Sally Shorter has a shortcut for any geoboard polygon with exactly four pegs on the boundary. All you have to tell her is how many pegs are in the interior and she can use her formula to find the are immediately. Frashy Shortest says she has the best formula in which you make any polygon on the geoboard and tell her both the number of pegs in the interior and the number of pegs on the boundary and her formula will give you the area immediately.

Your goal in this POW is
In (pegs) 8 10 15 16
Out(area) 6 7 9.5 10

Considering that I had divided by two in my previous formulas I decided to divide the amount of pegs on the boundary and see if I could add something to it to make it apply to my In-Out table. After doing so I realized that my formula was almost as one of my formulas in 1c. In my formula a represents the number of pegs on the boundary and b represents the area. This is my formula a/2 +2=b. My formula is correct because I placed in the numbers into my formula and it had the same results.

Question #2 a-c

2a.

Evaluation

This POW somewhat difficult to explain because you could find the formulas very quickly after doing the Table which made it hard to explain how you got the answer. I learned that when you want to make a formula and have different variables its good to use a chart to find their relation. I also learned that these formulas only apply to polygons because if you try to plug in a shape that isn’t a polygon you will get a wrong answer. To change this problem I would make it so that the person doing it would have to find the formula that works for polygons with 1-5 pegs. I would also add that if your formula applies to all shapes. Overall this POW was easy because what you had to do was repetitive and