Difference between revisions of "Dodecagon"

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A regular dodecagon can be seen below:
 
A regular dodecagon can be seen below:
  
[asy]
+
<asy>
 
for(int i = 0; i <= 11; ++i) {
 
for(int i = 0; i <= 11; ++i) {
 
draw(dir(360/12*i)--dir(360/12*(i + 1)));
 
draw(dir(360/12*i)--dir(360/12*(i + 1)));
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draw(A--G);
 
draw(A--G);
 
draw(Circle(O,1));
 
draw(Circle(O,1));
[/asy]
+
</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>.
 
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>.
  

Revision as of 12:05, 15 June 2018

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

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--G); 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 $OA$.

See Also

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