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## Aadarsh 3 years ago Area of a regular octagon is 4(root 2 + 1) square units. Find its side.

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1. Aadarsh

|dw:1334302795177:dw|

2. Aadarsh

@Taufique bhai, please help.

3. Aadarsh

Let the side of octagon be "x" units.

4. fractal5

$4\sqrt{2+1}$ or $4\sqrt{2}+1$

5. Aadarsh

|dw:1334303032758:dw| @fractal5 , the first one

6. fractal5

are you sure, because that is = $4\sqrt{3}$

7. Aadarsh

Now, |dw:1334303202974:dw|

8. Aadarsh

The actual area is :|dw:1334303237350:dw|

9. fractal5

Area = ( 2 + 2√2 )*(x^2) where x is the side length

10. Taufique

in the regular octagon.there will be 8 equilateral triangle hence let the side is x. then area of octagon=8*area of one equilateral triangle =$8\times \sqrt{3}\div 4 (x ^{2})$..find x.

11. Aadarsh

@Taufique bhai, can u say the answer?

12. fractal5

Are you sure they are equilateral? I think in a hexagon they are equil. not octagon

13. Aadarsh

Even I am in doubt whther we will get 8 equilateral traingles or not.

14. fractal5

Just solve the formula I gave

15. Aadarsh

@fractal5 , u r rite. I got it. Can u say how u got it?

16. Aadarsh

@fractal5,can u plz explain the formula how u got it?

17. Aadarsh

@gurvinder bhai, can u explain the formula?

18. Taufique

@Aadarsh fractal is right .. |dw:1334303786166:dw|

19. Aadarsh

Okay. But can u explain the formula which @fractal5 used? plzzzzzzzz

20. Aadarsh

@Taufique bhai, u der?

21. Taufique

|dw:1334304124446:dw| find its area and multiply it by 8 and put it equal to given area in your question...

22. Aadarsh

But, now can u explain the nest step? The height and side in terms of "x"?

23. Taufique

Aadarsh wait.

24. Aadarsh

Okay bhai. I will be coming in 15 minutes after lunch.

25. Taufique

|dw:1334304950665:dw| put the value of tan67.5 deg equal to

26. Aadarsh

Okay bhai. But how to obtain value of tan 67.5?

27. Taufique

tan67.5deg=root2+1 put there and find x

28. Taufique

|dw:1334305364185:dw|

29. Taufique

@Aadarsh ab kho bhai koi problem.. sorry kam kar rha tha college ka project tha.

30. Taufique

Aadarsh khan ho.

31. Taufique

|dw:1334305876442:dw| find tan67.5 from here.

32. Aadarsh

But abhi isko solve kaise karenge?

33. Taufique

tan67.5=x let |dw:1334306229613:dw| x=root2+1 is only possible because 67.5 is in first quadrant and in first quadrant tan ins positive.hence neglect negative value(1-root2)

34. Aadarsh

OH yeah I got it. Thanks bhai!!!!!!!

35. Taufique

ji han vai apko v dhanyabad samajne k liye..

36. Aadarsh

Thanks ji.

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