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And last, if you had the number on the interior, and the number on the boundary, you could get the area.
The first two equations, were a preparation for the final, building up towards the complete idea. This helped, because I could complete the first two pretty quickly.
For Freddie I drew a 3 column T-Table, with a drawing of the figure, the number of Pegs (in), and the Area (out). I looked for a pattern between the in and the out, and quickly found one that made sense, and I worked it into a formula. I got X/2-1=Y. Where X is IN (number of pegs) and Y is OUT (Area). This works in all shapes with no interior pegs, like Freddie described...
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