## OpenSessame Group Title Find the area of the regular polygon. Give the answer to the nearest tenth. Decagon with a side of 4 cm. one year ago one year ago

1. OpenSessame

2. OpenSessame

@koymoi can you help?

3. OpenSessame

I know the answer i just dont get how to get there.

4. koymoi

do you know how many sides a decagon has

5. OpenSessame

10?

6. koymoi

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

|dw:1376882655959:dw|

8. OpenSessame

10

9. koymoi

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

Okay...

11. koymoi

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

144

13. koymoi

|dw:1376883184207:dw|

14. koymoi

|dw:1376883372359:dw|

15. OpenSessame

No clue

16. koymoi

|dw:1376883474402:dw|

17. OpenSessame

okay so the angle would be 72?

18. koymoi

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19. OpenSessame

Uhm...Its the same length on both sides...right?

20. koymoi

right.

21. OpenSessame

Would i use trig?

22. koymoi

yes you would;)

23. OpenSessame

|dw:1376884123072:dw|

24. OpenSessame

Wouldnt you need to know the interior angle though?

25. OpenSessame

Wait its regular so all of them are the same!

26. koymoi

that triangle is isosceles triangle, not equilateral triangle

27. OpenSessame

But its a regular decagon...

28. OpenSessame

|dw:1376884408466:dw|

29. OpenSessame

|dw:1376884457513:dw|

30. koymoi

yes thats why its isosceles. the only way to make it equilateral is when all the interior angles equals to 60 degrees.

31. OpenSessame

OHH...

32. OpenSessame

I meant the outside angles lol

33. OpenSessame

I got 6.47

34. koymoi

|dw:1376884560108:dw|

35. OpenSessame

OHH...6.15?

36. koymoi

|dw:1376884812109:dw|

37. koymoi

and since we have 10 of them triangles, so you just multiply by 10 to get the area of the decagon.

38. OpenSessame

1.9?

39. koymoi

what is tan72 ?

40. OpenSessame

3.07768

41. koymoi

|dw:1376885258455:dw|

42. koymoi

now times 10

43. koymoi

and dont forget to round it to the nearest tenth

44. OpenSessame

61.55?

45. OpenSessame

I think i get it now since i know the final answer. THANKS:)