Find the area of the hexagon with given conditions [closed]

0

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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.

geometry

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edited Jan 18 at 6:54

Shane Dizzy Sukardy

asked Jan 18 at 6:41

Shane Dizzy SukardyShane Dizzy Sukardy

60819

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Henrik, Claude Leibovici, heropup, Lee David Chung Lin, Martin Sleziak

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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.)
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  – Martin Sleziak
  Jan 18 at 11:15
  

  
  
  
  

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0

$begingroup$

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.

geometry

share|cite|improve this question

edited Jan 18 at 6:54

Shane Dizzy Sukardy

asked Jan 18 at 6:41

Shane Dizzy SukardyShane Dizzy Sukardy

60819

$endgroup$

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Henrik, Claude Leibovici, heropup, Lee David Chung Lin, Martin Sleziak

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  

  
  
  
  

add a comment | 

0

0

0

$begingroup$

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.

geometry

share|cite|improve this question

edited Jan 18 at 6:54

Shane Dizzy Sukardy

asked Jan 18 at 6:41

Shane Dizzy SukardyShane Dizzy Sukardy

60819

$endgroup$

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.

geometry

geometry

share|cite|improve this question

edited Jan 18 at 6:54

Shane Dizzy Sukardy

asked Jan 18 at 6:41

Shane Dizzy SukardyShane Dizzy Sukardy

60819

share|cite|improve this question

edited Jan 18 at 6:54

Shane Dizzy Sukardy

asked Jan 18 at 6:41

Shane Dizzy SukardyShane Dizzy Sukardy

60819

share|cite|improve this question

share|cite|improve this question

edited Jan 18 at 6:54

Shane Dizzy Sukardy

edited Jan 18 at 6:54

Shane Dizzy Sukardy

edited Jan 18 at 6:54

Shane Dizzy Sukardy

asked Jan 18 at 6:41

Shane Dizzy SukardyShane Dizzy Sukardy

60819

asked Jan 18 at 6:41

Shane Dizzy SukardyShane Dizzy Sukardy

60819

asked Jan 18 at 6:41

Shane Dizzy SukardyShane Dizzy Sukardy

60819

60819

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Henrik, Claude Leibovici, heropup, Lee David Chung Lin, Martin Sleziak

If this question can be reworded to fit the rules in the help center, please edit the question.

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Henrik, Claude Leibovici, heropup, Lee David Chung Lin, Martin Sleziak

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  

  
  
  
  

$begingroup$
What is surd form?
$endgroup$
– El borito
Jan 18 at 6:58

$begingroup$
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

$begingroup$
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

$begingroup$
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

add a comment | 

2 Answers
2

active

oldest

votes

1

$begingroup$

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.

share|cite|improve this answer

answered Jan 18 at 11:07

SaeeSaee

387

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add a comment | 

0

$begingroup$

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

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

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.

share|cite|improve this answer

answered Jan 18 at 7:33

guchiheguchihe

1188

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add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

1

$begingroup$

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.

share|cite|improve this answer

answered Jan 18 at 11:07

SaeeSaee

387

$endgroup$

add a comment | 

1

$begingroup$

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.

share|cite|improve this answer

answered Jan 18 at 11:07

SaeeSaee

387

$endgroup$

add a comment | 

1

1

1

$begingroup$

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.

share|cite|improve this answer

answered Jan 18 at 11:07

SaeeSaee

387

$endgroup$

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.

share|cite|improve this answer

answered Jan 18 at 11:07

SaeeSaee

387

share|cite|improve this answer

share|cite|improve this answer

answered Jan 18 at 11:07

SaeeSaee

387

answered Jan 18 at 11:07

SaeeSaee

387

answered Jan 18 at 11:07

SaeeSaee

387

387

add a comment | 

add a comment | 

0

$begingroup$

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

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

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.

share|cite|improve this answer

answered Jan 18 at 7:33

guchiheguchihe

1188

$endgroup$

add a comment | 

0

$begingroup$

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

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

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.

share|cite|improve this answer

answered Jan 18 at 7:33

guchiheguchihe

1188

$endgroup$

add a comment | 

0

0

0

$begingroup$

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

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

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.

share|cite|improve this answer

answered Jan 18 at 7:33

guchiheguchihe

1188

$endgroup$

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

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

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.

share|cite|improve this answer

answered Jan 18 at 7:33

guchiheguchihe

1188

share|cite|improve this answer

share|cite|improve this answer

answered Jan 18 at 7:33

guchiheguchihe

1188

answered Jan 18 at 7:33

guchiheguchihe

1188

answered Jan 18 at 7:33

guchiheguchihe

1188

1188

add a comment | 

add a comment | 

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