anonymous
  • anonymous
Find the area of the regular polygon. Give the answer to the nearest tenth. Decagon with a side of 4 cm.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Can you help please??
anonymous
  • anonymous
@koymoi can you help?
anonymous
  • anonymous
I know the answer i just dont get how to get there.

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anonymous
  • anonymous
do you know how many sides a decagon has
anonymous
  • anonymous
10?
anonymous
  • anonymous
yes, now how many triangles of the same shape can we get from a decagon? I will give you lil bit hint in the pic below:
anonymous
  • anonymous
|dw:1376882655959:dw|
anonymous
  • anonymous
10
anonymous
  • anonymous
ok, now what we need to do is to figure out how to work out the area of one of those little triangle.
anonymous
  • anonymous
Okay...
anonymous
  • anonymous
to do that, we need to get each inner angle of the decagon first. use this formula: 180(n-2)├Ěn n=sides in this case, since decagon has 10 sides, so n=10
anonymous
  • anonymous
144
anonymous
  • anonymous
|dw:1376883184207:dw|
anonymous
  • anonymous
|dw:1376883372359:dw|
anonymous
  • anonymous
No clue
anonymous
  • anonymous
|dw:1376883474402:dw|
anonymous
  • anonymous
okay so the angle would be 72?
anonymous
  • anonymous
|dw:1376883661743:dw|
anonymous
  • anonymous
Uhm...Its the same length on both sides...right?
anonymous
  • anonymous
right.
anonymous
  • anonymous
Would i use trig?
anonymous
  • anonymous
yes you would;)
anonymous
  • anonymous
|dw:1376884123072:dw|
anonymous
  • anonymous
Wouldnt you need to know the interior angle though?
anonymous
  • anonymous
Wait its regular so all of them are the same!
anonymous
  • anonymous
that triangle is isosceles triangle, not equilateral triangle
anonymous
  • anonymous
But its a regular decagon...
anonymous
  • anonymous
|dw:1376884408466:dw|
anonymous
  • anonymous
|dw:1376884457513:dw|
anonymous
  • anonymous
yes thats why its isosceles. the only way to make it equilateral is when all the interior angles equals to 60 degrees.
anonymous
  • anonymous
OHH...
anonymous
  • anonymous
I meant the outside angles lol
anonymous
  • anonymous
I got 6.47
anonymous
  • anonymous
|dw:1376884560108:dw|
anonymous
  • anonymous
OHH...6.15?
anonymous
  • anonymous
|dw:1376884812109:dw|
anonymous
  • anonymous
and since we have 10 of them triangles, so you just multiply by 10 to get the area of the decagon.
anonymous
  • anonymous
1.9?
anonymous
  • anonymous
what is tan72 ?
anonymous
  • anonymous
3.07768
anonymous
  • anonymous
|dw:1376885258455:dw|
anonymous
  • anonymous
now times 10
anonymous
  • anonymous
and dont forget to round it to the nearest tenth
anonymous
  • anonymous
61.55?
anonymous
  • anonymous
I think i get it now since i know the final answer. THANKS:)

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