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Draw a regular hexagon and a regular dodecagon (12-sided polygon) inscribed in a circle. If the area of the dodecagon is $12~\text{cm}^2$, find the area of the hexagon in $\text{cm}^2$. (Express your answer in surd form.)

Please solve this. This is the only one problem in my geometry paper that can't be solved by us.

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closed as off-topic by Henrik, Claude Leibovici, heropup, Lee David Chung Lin, Martin Sleziak Jan 18 at 11:15

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  • $\begingroup$ What is surd form? $\endgroup$ – El borito Jan 18 at 6:58
  • $\begingroup$ It is the number under radical sign that can't be simplified anymore $\endgroup$ – Shane Dizzy Sukardy Jan 18 at 7:00
  • $\begingroup$ Your question was put on hold, the message above (and possibly comments) should give an explanation why. (In particular, this link might be useful.) You might try to edit your question to address these issues. Note that the next edit puts your post in the review queue, where users can vote whether to reopen it or leave it closed. (Therefore it would be good to avoid minor edits and improve your question as much as possible with the next edit.) $\endgroup$ – Martin Sleziak Jan 18 at 11:15
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Here is my figure: (https://i.stack.imgur.com/pQbFc.jpg) See if you can find the ratio of the areas of ABCD and BDC. Then you are done.

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In the first figure, all the lines red has the same length, as well as the black lines.

enter image description here

Note that $(ABO)=1 = (BCO)$. Also, is not difficult to see that, in the $\triangle ABO$:

enter image description here

with $\triangle ABC \cong \triangle AOK$, where $K$ is the circumcenter of $ABO$, so you can compute $(ABC)$ and then $(ACO)$ and finally multiply by 6.

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