document.write( "Question 1163742: The figure shows a 2×2×2 cube ABCDEFGH, as well as midpoints I and J of its edges DH and BF. It so happens that C,I,E, and J all lie in a plane. Can you justify this statement? What kind of figure is quadrilateral CIEJ, and what is its area? Is it possible to obtain a polygon with a larger area by slicing the cube with a different plane? If so, show how to do it. If not, explain whyit is not possible. \n" ); document.write( "
Algebra.Com's Answer #787947 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
I did that problem a week or so ago. \r\n" );
document.write( "Question 1163283\r\n" );
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document.write( "The figure ABOVE shows a 2 × 2 × 2 cube ABCDEFGH, as well as midpoints I and\r\n" );
document.write( "J of its edges DH and BF. It so happens that C , I , E , and J all lie in a\r\n" );
document.write( "plane. Can you justify this statement?
Yes I can. A quadrilateral is coplanar if and only if the sum of its\r\n" );
document.write( "interior angles is 360°.  The plane of square ABFE is perpendicular to the\r\n" );
document.write( "plane of BCGF. If two planes are perpendicular, then any angle whose sides\r\n" );
document.write( "are in the two planes are 90°, so ∠CJE=90°  Thus EJ ∥ CJ and\r\n" );
document.write( "similarly the other 4 interior angles of quadrilateral CIEJ also 90°. Thus\r\n" );
document.write( "quadrilateral CIEF is also a rectangle.  Thus the sum of the interior angles is \r\n" );
document.write( "4∙90° = 360°.
What kind of figure is quadrilateral CIEJ,
It is not only a rectangle but also a square because right triangles ΔIHE,\r\n" );
document.write( "ΔBJC, ΔJFE, ΔDIC are all congruent and their longer legs are its sides.
and what is its area?
Congruent right triangles ΔIHE, ΔBJC, ΔJFE, ΔDIC all have hypotenuses 2 and\r\n" );
document.write( "shorter legs 1, so by the Pythagorean theorem, each side of square CIEJ is\r\n" );
document.write( "√5.  Therefore the area of square CIEJ is 5.
Is it possible to obtain a polygon with a larger area by slicing the cube
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document.write( "with a different plane? If so, show how to do it. If not, explain why it is
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document.write( "not possible.
Yes, it is possible. CDEF and BGHA are rectangles with length 2√2 and width\r\n" );
document.write( "2. So their areas are 4√2 which is approximately 5.656854249 > 5. \r\n" );
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document.write( "Edwin
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