Dodecagon

A dodecagon

A dodecagon or 12-gon is a shape with 12 sides and 12 corners.

Regular dodecagon

All sides of a regular dodecagon are the same length. Each corner is 150°. All corners added together equal 1800°.

Area

The amount of space a regular dodecagon takes up is

[math]\displaystyle{ \begin{align} A & = 3 \cot\left(\frac{\pi}{12} \right) a^2 = 3 \left(2+\sqrt{3} \right) a^2 \\ & \approx 11{,}19615\,a^2. \end{align} }[/math]

The variable A represents the area, and the variable a represents the apothem.

Perimeter

The perimeter of a regular dodecagon is

[math]\displaystyle{ \begin{align} P = 12s \end{align} }[/math]

The variable P represents the perimeter, and the variable s represents one side.

Dodecagon Media

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  Three squares of sides R can be cut and rearranged into a dodecagon of circumradius R, yielding a proof without words that its area is 3R2

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  en:12-cube, A11 projection

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  12-gon rhombic dissection-size2

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  12-gon rhombic dissection2-size2

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  12-gon rhombic dissection3-size2

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  12-gon rhombic dissection4-size2

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  12-gon rhombic dissection5-size2

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  Dissection of isotoxal polygon into rhombi, center alternating two types of rhombs

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  6-cube hexeract graph

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  Rhombic dissected dodecagon