The number of diagonals (we'll label diagonals as "d") that can be drawn in a polygon of "n" sides is given by the formula:
d =
n(n-3)
________
2
Ok, so that fraction doesn't look very good. I'm trying to say that the formula for diagnoals in a polygon is n(n-3) over 2.
Let's use your 12 sided figure as our example:
12(12-3)/2 <---- this is a fraction of 12(12-3) over 2
12(9)/2 is the same as 12 x 9 over 2
108/2 is the same as 108 over 2
108/ 2 = 54
Soooooooo we can draw 54 diagonals in a 12 sided figure. cool.
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