dodecagon
12 sided polygon
A dodecagon is a polygon that has twelve sides and twelve angles. The prefix dodeca comes from the Greek word dōdeka which means twelve, hence the name dodecagon.
To find the interior angle of a regular dodecagon, we can use the formula:
Interior Angle = (n-2) x 180° / n
Where n is the number of sides (in this case, n = 12)
Plugging in the values, we get:
Interior Angle = (12-2) x 180° / 12 = 150°
Therefore, the interior angle of a regular dodecagon is 150 degrees.
To find the perimeter (or the total length of all sides) of a regular dodecagon, we can use the formula:
Perimeter = 12 x s
Where s is the length of one side.
If we are given the radius (r) of a regular dodecagon, we can find the length of one side (s) using the formula:
s = 2r x sin (180°/12)
Where sin (180°/12) is the sine of the interior angle of a regular dodecagon.
Once we find the length of one side, we can plug it into the perimeter formula to find the total length of all sides.
In geometry, there are many properties and theorems related to dodecagons, such as the sum of interior angles, the area formula, and the circumradius formula.
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