anonymous
  • anonymous
What is the area of a regular decagon with a radius of 8 centimeters?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
did you get this yet?
anonymous
  • anonymous
No, I can't find a formula that I understand.
anonymous
  • anonymous
do you know trig or are you using something else?

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anonymous
  • anonymous
Do not know trig! Trying my hardest, I have difficulties with even simple math.
anonymous
  • anonymous
i am not sure i can do it without trig. maybe Anwar?
anonymous
  • anonymous
oops he just left.
anonymous
  • anonymous
:/ Can you explain it to me? If you can explain the formula, I can do that.
anonymous
  • anonymous
ok you need to think of splitting it up in to right triangles. you will have twenty of them.
anonymous
  • anonymous
wait i have a better idea, because i see this one involves trig as well. so we might as well do this. the formula for the area of a triangle is \[\frac{1}{2}bcsin(A)\] where A is the angle between the sides. in this case the sides are both of length 8 and the angle is 360/10=36
anonymous
  • anonymous
so unless i miss my guess each of these 10 triangles (not 20, just ten) has area \[32sin(36)=18.809\]
anonymous
  • anonymous
multiply by 10 to get the total area. now i am going to check to see if this is correct. but i cannot see a way to do it without using some trig.
anonymous
  • anonymous
Thank you for trying so hard, though, and this I can understand fairly easy.
anonymous
  • anonymous
welcome, but don't quote me!
anonymous
  • anonymous
yea but i think i am wrong. i will keep trying.
anonymous
  • anonymous
ok let me try again. is this for a trig class?
anonymous
  • anonymous
in any case break this thing up into 20 right triangles, each with hypotenuse 8. the small angle between the long sides of those triangle is 18 degrees because it is 360/20
anonymous
  • anonymous
call the long side of those triangles b \[cos(18)=\frac{b}{10}\] so the long side is \[b=10cos(18)=9.51\] rounded. the last side we find by pythagoras since we know the hypotenuse and the long side. the short side is \[\sqrt{10^2-9.51^2}=3.09\] rounded.
anonymous
  • anonymous
the area of each of those twenty triangles is therefore \[\frac{1}{2} 9.21 \times3.09\]
anonymous
  • anonymous
since there are twenty of them just compute \[10\times 9.21 \times 3.09\]
anonymous
  • anonymous
i know this answer is correct (i mean i know the area is) because i did checked it here: http://www.cleavebooks.co.uk/scol/calpolyg.htm
anonymous
  • anonymous
i see that i used 10 instead of 8. you should use 8. but i also got the same answer using the sine method so forget it.

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