IMP 2 POW 8 Essay -- Math Mathmatics Problems

Problem StatementMy task was to find 3 equations, that would give me an answer, if I had certain information. The initiatory was to find one that if you knew that there were four pegs on the boundary, and none on the interior, you could calculate the area. The second was if you knew that there were 4 pegs on the boundary, and you knew how many were on the interior, you could get the area. And last, if you had the number on the interior, and the number on the boundary, you could get the area.ProcessThe first two equations, were a preparation for the final, building up towards the lie with 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 innovation 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 whole cabood le in all shapes with no interior pegs, like Freddie described. I attached this T-Table.For Sally I followed my luck of the 3 column T-Table, and drew another with the very(prenominal) guidelines. The figure, the interior pegs (in), and the area (out). After I filled in a few figures, and their properties, I noticed a pattern, and not long after, a formula, which worked for them. It was X+1=Y. This T-Table is also attached.Now...the next was not so easy. Frashys required a long thought process, an...