document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165480>Question 1165480</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Find the area of a hexagon with a square having an area of 72 sq. cm. inscribed in a circle which is inscribed in a hexagon.<BR>\n" );
document.write( "a. 124.71 sq. cm. b. 150.26 sq. cm. c. 150.35 sq. cm. d. 130.77 sq. cm. </SPAN>\n" );
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document.write( "Note the statement of the problem should specify a REGULAR hexagon; without that, the problem is not defined well enough to get an answer.<br><BR>\n" );
document.write( "Area of square which is inscribed in the circle: 72<br><BR>\n" );
document.write( "Side of square: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2872%29+=+6%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2872%29+=+6%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Diagonal of square = diameter of circle: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2Asqrt%282%29%29%2Asqrt%282%29+=+12 ALIGN=MIDDLE  ALT=\"%286%2Asqrt%282%29%29%2Asqrt%282%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The circle is inscribed in the hexagon; the diameter of the circle is the distance from the middle of one side of the hexagon to the middle of the opposite side.<br><BR>\n" );
document.write( "View the hexagon as being composed of 6 equilateral triangles.  The radius of the circle, length 12/2=6, is the long leg of a 30-60-90 right triangle in which the hypotenuse is the length of one side of one of those equilateral triangles.<br><BR>\n" );
document.write( "Side length of hexagon = side length of one of the equilateral triangles = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A%282%2Fsqrt%283%29%29+=+12%2Fsqrt%283%29+=+4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"6%2A%282%2Fsqrt%283%29%29+=+12%2Fsqrt%283%29+=+4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Area of hexagon = area of 6 equilateral triangles = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28%28s%5E2%2Asqrt%283%29%29%2F4%29+=+6%28%2848sqrt%283%29%29%2F4%29+=+72sqrt%283%29 ALIGN=MIDDLE  ALT=\"6%28%28s%5E2%2Asqrt%283%29%29%2F4%29+=+6%28%2848sqrt%283%29%29%2F4%29+=+72sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 124.71 to 2 decimal places.<br><BR>\n" );
document.write( "ANSWER: a. 124.71 sq cm<br><BR>\n" );
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