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OpenSessame

  • 2 years ago

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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  1. OpenSessame
    • 2 years ago
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    Can you help please??

  2. OpenSessame
    • 2 years ago
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    @koymoi can you help?

  3. OpenSessame
    • 2 years ago
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    I know the answer i just dont get how to get there.

  4. koymoi
    • 2 years ago
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    do you know how many sides a decagon has

  5. OpenSessame
    • 2 years ago
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    10?

  6. koymoi
    • 2 years ago
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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:

  7. koymoi
    • 2 years ago
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    |dw:1376882655959:dw|

  8. OpenSessame
    • 2 years ago
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    10

  9. koymoi
    • 2 years ago
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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.

  10. OpenSessame
    • 2 years ago
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    Okay...

  11. koymoi
    • 2 years ago
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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

  12. OpenSessame
    • 2 years ago
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    144

  13. koymoi
    • 2 years ago
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    |dw:1376883184207:dw|

  14. koymoi
    • 2 years ago
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    |dw:1376883372359:dw|

  15. OpenSessame
    • 2 years ago
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    No clue

  16. koymoi
    • 2 years ago
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    |dw:1376883474402:dw|

  17. OpenSessame
    • 2 years ago
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    okay so the angle would be 72?

  18. koymoi
    • 2 years ago
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    |dw:1376883661743:dw|

  19. OpenSessame
    • 2 years ago
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    Uhm...Its the same length on both sides...right?

  20. koymoi
    • 2 years ago
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    right.

  21. OpenSessame
    • 2 years ago
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    Would i use trig?

  22. koymoi
    • 2 years ago
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    yes you would;)

  23. OpenSessame
    • 2 years ago
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    |dw:1376884123072:dw|

  24. OpenSessame
    • 2 years ago
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    Wouldnt you need to know the interior angle though?

  25. OpenSessame
    • 2 years ago
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    Wait its regular so all of them are the same!

  26. koymoi
    • 2 years ago
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    that triangle is isosceles triangle, not equilateral triangle

  27. OpenSessame
    • 2 years ago
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    But its a regular decagon...

  28. OpenSessame
    • 2 years ago
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    |dw:1376884408466:dw|

  29. OpenSessame
    • 2 years ago
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    |dw:1376884457513:dw|

  30. koymoi
    • 2 years ago
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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.

  31. OpenSessame
    • 2 years ago
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    OHH...

  32. OpenSessame
    • 2 years ago
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    I meant the outside angles lol

  33. OpenSessame
    • 2 years ago
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    I got 6.47

  34. koymoi
    • 2 years ago
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    |dw:1376884560108:dw|

  35. OpenSessame
    • 2 years ago
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    OHH...6.15?

  36. koymoi
    • 2 years ago
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    |dw:1376884812109:dw|

  37. koymoi
    • 2 years ago
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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.

  38. OpenSessame
    • 2 years ago
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    1.9?

  39. koymoi
    • 2 years ago
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    what is tan72 ?

  40. OpenSessame
    • 2 years ago
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    3.07768

  41. koymoi
    • 2 years ago
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    |dw:1376885258455:dw|

  42. koymoi
    • 2 years ago
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    now times 10

  43. koymoi
    • 2 years ago
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    and dont forget to round it to the nearest tenth

  44. OpenSessame
    • 2 years ago
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    61.55?

  45. OpenSessame
    • 2 years ago
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    I think i get it now since i know the final answer. THANKS:)

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