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Difference between revisions of "Dodecagon"

 
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A dodecagon is a 12-sided polygon.
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A '''dodecagon''' is a 12-sided [[polygon]]. The sum of its internal [[angle]]s is <math>1800^{\circ}</math>. Each of its exterior angles has measure  <math>30^{\circ}</math>.
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A regular dodecagon can be seen below:
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<asy>
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for(int i = 0; i <= 11; ++i) {
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draw(dir(360/12*i)--dir(360/12*(i + 1)));
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}
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pair A,B,C,D,E,F,G,H,I,J,K,L;
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A=dir(360/12*0);
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B=dir(360/12*1);
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C=dir(360/12*2);
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D=dir(360/12*3);
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E=dir(360/12*4);
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F=dir(360/12*5);
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G=dir(360/12*6);
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H=dir(360/12*7);
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I=dir(360/12*8);
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J=dir(360/12*9);
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K=dir(360/12*10);
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L=dir(360/12*11);
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label("A",A,dir(0));
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label("B",B,dir(30));
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label("C",C,dir(60));
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label("D",D,dir(90));
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label("E",E,dir(120));
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label("F",F,dir(150));
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label("G",G,dir(180));
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label("H",H,dir(210));
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label("I",I,dir(240));
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label("J",J,dir(270));
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label("K",K,dir(300));
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label("L",L,dir(330));
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draw(dir(360/12*0)--dir(360/12*6));
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dot((dir(360/12*0)+dir(360/12*6))/2);
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pair O = (dir(360/12*0)+dir(360/12*6))/2;
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label("O",O,S);
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draw(A--O);
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draw(Circle(O,1));
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</asy>
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The area of a regular dodecagon can be calculated by the formula <math>3R^2</math>, where <math>R</math> is the circumradius of the dodecagon. In this case, <math>R</math> would be <math>OA</math>. Also, each small triangle (<math>AOB</math>, <math>BOC</math>, etc.) is congruent, so <math>\angle AOB=\angle BOC=\angle COD</math> (etc) <math>=30^{\circ}</math>.
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==See Also==
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* [[Polygon]]
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* [[Geometry]]
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[[Category:Geometry]]
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{{stub}}

Latest revision as of 12:08, 15 June 2018

A dodecagon is a 12-sided polygon. The sum of its internal angles is $1800^{\circ}$. Each of its exterior angles has measure $30^{\circ}$.

A regular dodecagon can be seen below:

[asy] for(int i = 0; i <= 11; ++i) { draw(dir(360/12*i)--dir(360/12*(i + 1))); } pair A,B,C,D,E,F,G,H,I,J,K,L; A=dir(360/12*0); B=dir(360/12*1); C=dir(360/12*2); D=dir(360/12*3); E=dir(360/12*4); F=dir(360/12*5); G=dir(360/12*6); H=dir(360/12*7); I=dir(360/12*8); J=dir(360/12*9); K=dir(360/12*10); L=dir(360/12*11); label("A",A,dir(0)); label("B",B,dir(30)); label("C",C,dir(60)); label("D",D,dir(90)); label("E",E,dir(120)); label("F",F,dir(150)); label("G",G,dir(180)); label("H",H,dir(210)); label("I",I,dir(240)); label("J",J,dir(270)); label("K",K,dir(300)); label("L",L,dir(330)); draw(dir(360/12*0)--dir(360/12*6)); dot((dir(360/12*0)+dir(360/12*6))/2); pair O = (dir(360/12*0)+dir(360/12*6))/2; label("O",O,S); draw(A--O); draw(Circle(O,1)); [/asy] The area of a regular dodecagon can be calculated by the formula $3R^2$, where $R$ is the circumradius of the dodecagon. In this case, $R$ would be $OA$. Also, each small triangle ($AOB$, $BOC$, etc.) is congruent, so $\angle AOB=\angle BOC=\angle COD$ (etc) $=30^{\circ}$.

See Also

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