Question 183969
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Draw a line that passes through one corner of the orginal acre plot at a 45 degree angle to an adjacent side of the original acre plot.  Repeat this process at each corner.  The four lines will intersect in four points forming the corners of a new, larger square rotated 45 degrees from the original.


If you assume that the sides of the original square were 1 unit in length, then the area of the original square is 1.  Superimposing the new, larger square over the original square creates four isoceles right triangles with hypotenuse measuring 1.  Each leg of these triangles is therefore *[tex \Large \frac{sqrt{2}}{2}] (Proof left as an exercise for the student).  Each leg of one of these triangles forms one-half of the side of the new square, so the length measure of the side is *[tex \Large \frac{sqrt{2}}{2} + \frac{sqrt{2}}{2} = sqrt{2}] and therefore the area is 2, exactly twice the are of the original square.


Write back if you absolutely need me to draw a picture.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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