Difference between revisions of "Dodecagon"

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) $=30^{\circ}$ .

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Difference between revisions of "Dodecagon"

Latest revision as of 12:08, 15 June 2018

See Also

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-A '''dodecagon''' is a 12-sided [[polygon]]. The sum of its internal [[angle]]s is <math>1800^{\circ}</math>.
+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>.
+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 <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>.
 ==See Also==