Formula: 0.5*(n2-3n) = diagonals whereas n is the number of sides
So if: 0.5*(n2-3n) = 54
Then: n2-3n-108 = 0
Solving the above quadratic equation gives n a value of -9 and 12
It has to be 12 which means it is a dodecagon polygon
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Please note that the diagonals cross one another at right angles, and bisect one another. You should draw a diagram to visualize this. From this center point, where the diagonals cross, you have a RIGHT TRIANGLE that involves half of one diagonal, half of the other diagonal, and one of the sides of the rhombus. This lets you use the Pythagorean Theorem to solve for the length of the side.
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