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Topic: Rectangle Area
Replies: 11   Last Post: Jan 14, 2010 1:01 PM

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narasimham

Posts: 2,537
Registered: 12/6/04
Re: Rectangle Area
Posted: Jan 14, 2010 1:01 PM
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On Jan 5, 8:29 pm, Avni Pllana <avni...@hotmail.com> wrote:
> Let ABCD be an arbitrary rectangle. Let DEFG be a rectangle such that E is an arbitrary point on the line through AB, and FG passes through C. If S1 is the area of ABCD, determine the area S2 of DEFG.
>
> Best regards,
>    Avni


Tilting of rigid rectangle DABC to position DEFG by an angular
rotation t about fulcrum D creates four similar triangles. If DAE =
angle t, the new sides so obtained DE and to DG are respectively
multiplied and divided by the same sec(t), making the product area
constant.

Best Regards,
Narasimham

PS: ( Quite lateral to this post ! ) I wonder if the area of these two
rectangles would still remain constant in hyperbolic geometry with two
circular arc sides,when viewed as inversions about an arbitrary circle
centered at fulcrum D.



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