# 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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