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

 Messages: [ Previous | Next ]
 Philippe 92 Posts: 44 Registered: 5/10/06
Re: Rectangle Area
Posted: Jan 11, 2010 7:35 AM

Hi Avni,

> I think there is a simpler dissection solution to the problem.
> Using the figure you posted as reference, we observe that DCG
> is congruent to EMF. Hence area(DEFG) = area(DEMC).
> Since length(AB) = length(EM), it follows
>
> area(ABCD) = area(DEMC),
>
> therefore S2 = S1.
> So we need only the additional point M for the proof.

I agree that nothing else is required for the *proof*.

The other points and lines on my drawing are just the edges
of the 4 necessary pieces (blue, green, yellow, pink) in there
successive positions, when dissecting :
rectangle ABCD -> parallelogram EMCD -> rectangle DEFG by
1) translation of triangle DAE -> CBM
2) then translation of triangle EFM -> DGC
(of course the same dissection might be in reverse order
DEFG -> ABCD)

Best Regards.

PS. I finally found my old login at Drexel, so I can answer directly here.
There seems to be a problem with crossfeed of Drexel to usenet.
(geometry.puzzles is *declared* as a public usenet group.
This seeems then to be false...)

Date Subject Author
1/5/10 Avni Pllana
1/5/10 Steve B
1/5/10 Steve B
1/6/10 Avni Pllana
1/11/10 Peter Chang
1/11/10 Avni Pllana
1/11/10 Steve B
1/9/10 Avni Pllana
1/9/10 Avni Pllana
1/11/10 Philippe 92
1/12/10 Steve B
1/14/10 narasimham