Difference between revisions of "Dodecagon"
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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>. | ||
| − | 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. | + | |
| + | 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--G); | ||
| + | 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>. | ||
==See Also== | ==See Also== | ||
Revision as of 12:05, 15 June 2018
A dodecagon is a 12-sided polygon. The sum of its internal angles is 
.
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--G);
draw(Circle(O,1));
[/asy]
The area of a regular dodecagon can be calculated by the formula 
, where 
is the circumradius of the dodecagon. In this case, would be 
.
See Also
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