Dodecagon
In geometry, a dodecagon is any twelve-sided polygon or 12-gon.
Regular dodecagon
A regular dodecagon has Schläfli symbol {12} and can be constructed as a truncated hexagon, t{6}, or a twice-truncated triangle, tt{3}.
It has all sides of equal length and all angles equal to 150°. It has 12 lines of symmetry and rotational symmetry of order 12. Its Schläfli symbol is {12}.
The area of a regular dodecagon with side a is given by:
Or, if R is the radius of the circumscribed circle,
And, if r is the radius of the inscribed circle,
A simple formula for area (given the two measurements) is: 
where d is the distance between parallel sides.
Length d is the height of the dodecagon when it sits on a side as base, and the diameter of the inscribed circle.
By simple trigonometry, 
.
The perimeter for an inscribed dodecagon of radius 1 is 12√(2 - √3), or approximately 6.21165708246.
The perimeter for a circumscribed dodecagon of radius 1 is 24(2 – √3), or approximately 6.43078061835. Interestingly, this is double the value of the area of the inscribed dodecagon of radius 1.
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