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Thread: Area of A Quad

20090119, 17:54 #1
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Area of A Quad
I posted a similar puzzle once before, so if it looks familiar... The numbers are different, and the art is not nearly as good, but the difficulty should keep you busy for a little while.
The objective is to find the area of the shaded region [Gxnp]. The sides of the squares are 18 and 12. Good luck. Ricky

20090120, 00:42 #2
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Re: Area of A Quad
I get about <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">18.69 </span hide>sq units.
Methodology:
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">Calculated the length Gx by similar triangles 4.8 = 12*12/30
EG = 12
So Triangle EGx = 12 * 4.8 / 2 = 28.8
Defined the picture on an XY coord system.
A= (0,0) and E=(30,12) so line AE has slope = 0.4 and Int = 0
D = (18,18) and F=(30,0) so line DF has slope = 1.5 and Int = 45
Line AE and line DF intercept at n = (23.684..., 9.474..)
Thus length of perp from line GE to N has length 129.474... = 2.526...
Gp can be calc from similar triangles = 6*12/18 = 4 and thus Ep = GE  Gp = 12  4 = 8
Area of triangle pnE = EP * (len of line of GE perp to n) / 2 = (8 * 2.526..)/2 = 10.105...
Area of Quad Gxpn = Area of EGx  Area pnE = 28.8  10.105... = 18.9647...</span hide>
Steve

20090121, 14:29 #3
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Re: Area of A Quad
And this is posted in a forum categorised as, "Light Relief"??!!! <img src=/S/drop.gif border=0 alt=drop width=23 height=23>
Regards,
Rudi

20090121, 14:40 #4
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Re: Area of A Quad
Well, he could have asked for the area of the largest circle that can be formed, tangent to the sides of the quad.
Christopher Baldrey

20090121, 15:42 #5
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Re: Area of A Quad
Hmmm... <img src=/S/nope.gif border=0 alt=nope width=15 height=15>
I'd rather get on my quad and ride circles round the area of my large back yard. (Now that's light relief)! <img src=/S/grin.gif border=0 alt=grin width=15 height=15>Regards,
Rudi

20090121, 16:47 #6
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Re: Area of A Quad
If it must be tangent to all 4 sides, I think there is no answer as there is no circle that can be created, I think you can get various circles tangent to the various possibilities of 3 of the 4 sides...
Steve

20090121, 16:53 #7
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Re: Area of A Quad
That's why it wouldn't be light relief any more... <img src=/S/evilgrin.gif border=0 alt=evilgrin width=15 height=15>

20090121, 17:06 #8
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Re: Area of A Quad
I would think that would depend on how long it takes to realize the lack of a solution and the enjoyment of the puzzlesolving up until that point....
Steve

20090126, 17:50 #9
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Re: Area of A Quad
>And this is posted in a forum categorised as, "Light Relief"??!!!
Don't sweat it, Rudi
Steve works for a firm that massproduces aspirin. <img src=/S/headthrob.gif border=0 alt=headthrob width=15 height=15>

20090127, 07:40 #10
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Re: Area of A Quad
Thats GREAT to know!! <img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>
Regards,
Rudi