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 to find Frashy’s super formula but tou might want to begin with her friends formulas.

1 Begin with Freddy’s formula

a. Find a formula for the area of polygons with no pegs in the interior. The number of boundaries is the In and the Out is the area in the In-Out table.

b. Find a different formula that works for polygons with one peg in the interior.

c. Pick a number bigger than one and find the area with that number of pegs in the interior.

d. Do more cases like question c

2.Find Sally’s formula and others like it, as described in 2a through 2c.

a. Find a formula for the area of polygons with exactly four pegs on the boundary.

b. Pick a number either than four and find the area of polygons with that number of pegs on the boundary.

c. Do more cases like of 2b

When you have finished work on Questions 1 and 2, look for a super formula that works for all figures. Your formula should have two inputs and the output should be the area.
Question #1 a-d

a. I first started creating polygons on my geoboard paper with no interior pegs and found the number of exterior pegs and the area. After creating 6 shapes on my geoboard paper I created an in-out table.

In ( pegs)5 671014...
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