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Find the area of the regular polygon. Give the answer to the nearest tenth. Decagon with a side of 4 cm.
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Can you help please??
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@koymoi can you help?
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I know the answer i just dont get how to get there.
koymoi
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do you know how many sides a decagon has
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10?
koymoi
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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:
koymoi
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|dw:1376882655959:dw|
OpenSessame
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10
koymoi
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ok, now what we need to do is to figure out how to work out the area of one of those little triangle.
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Okay...
koymoi
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to do that, we need to get each inner angle of the decagon first. use this formula: 180(n-2)÷n n=sides in this case, since decagon has 10 sides, so n=10
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144
koymoi
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|dw:1376883184207:dw|
koymoi
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|dw:1376883372359:dw|
OpenSessame
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No clue
koymoi
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|dw:1376883474402:dw|
OpenSessame
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okay so the angle would be 72?
koymoi
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|dw:1376883661743:dw|
OpenSessame
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Uhm...Its the same length on both sides...right?
koymoi
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right.
OpenSessame
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Would i use trig?
koymoi
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yes you would;)
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|dw:1376884123072:dw|
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Wouldnt you need to know the interior angle though?
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Wait its regular so all of them are the same!
koymoi
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that triangle is isosceles triangle, not equilateral triangle
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But its a regular decagon...
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|dw:1376884408466:dw|
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|dw:1376884457513:dw|
koymoi
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yes thats why its isosceles. the only way to make it equilateral is when all the interior angles equals to 60 degrees.
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OHH...
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I meant the outside angles lol
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I got 6.47
koymoi
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|dw:1376884560108:dw|
OpenSessame
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OHH...6.15?
koymoi
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|dw:1376884812109:dw|
koymoi
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and since we have 10 of them triangles, so you just multiply by 10 to get the area of the decagon.
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1.9?
koymoi
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what is tan72 ?
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3.07768
koymoi
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|dw:1376885258455:dw|
koymoi
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now times 10
koymoi
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and dont forget to round it to the nearest tenth
OpenSessame
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61.55?
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I think i get it now since i know the final answer. THANKS:)