document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083475>Question 1083475</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A star shape is made from 6 congruent equilateral triangles and a regular hexagon. The star shape has an area of 96cm^2. What is the area of the regular hexagon? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697560 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"4\"><BR>\n" );
document.write( "Answer: <font color=red>48 square centimeters</font><BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "A drawing often helps solve the problem very easily<BR>\n" );
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document.write( "The red triangular exterior pieces are all equilateral triangles with some side length. <BR>\n" );
document.write( "We don't need to know what that side length is. It doesn't matter.\r<BR>\n" );
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document.write( "The area of one red equilateral triangle is some area A. <BR>\n" );
document.write( "There are 6 of these red triangles, so the red exterior triangular parts combine to a total area of 6*A. \r<BR>\n" );
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document.write( "The hexagon is composed of equilateral triangles as well. <BR>\n" );
document.write( "Each of these blue equilateral triangles is congruent to any outer red triangle because the side length is the same. <BR>\n" );
document.write( "Therefore, the 6 blue equilateral triangles composing this hexagon combine to get a total area of 6*A\r<BR>\n" );
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document.write( "The area of the star overall is 12*A because we have 6 blue triangles combining with the 6 red triangles. <BR>\n" );
document.write( "There is a total of 12 triangles.\r<BR>\n" );
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document.write( "To recap so far: <BR>\n" );
document.write( "Area of hexagon = 6*A<BR>\n" );
document.write( "Area of star = 12*A\r<BR>\n" );
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document.write( "The ratio of the two areas is<BR>\n" );
document.write( "R = (area of hexagon)/(area of star)<BR>\n" );
document.write( "R = (6A)/(12A)<BR>\n" );
document.write( "R = 1/2<BR>\n" );
document.write( "R = 0.5\r<BR>\n" );
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document.write( "Basically telling us the area of the hexagon is half that of the star. <BR>\n" );
document.write( "We can see this with a bit of algebra<BR>\n" );
document.write( "R = (area of hexagon)/(area of star)<BR>\n" );
document.write( "R*(area of star) = area of hexagon<BR>\n" );
document.write( "area of hexagon = R*(area of star)<BR>\n" );
document.write( "area of hexagon = 0.5*(area of star)\r<BR>\n" );
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document.write( "Now plug in the star's area<BR>\n" );
document.write( "area of hexagon = 0.5*(area of star)<BR>\n" );
document.write( "area of hexagon = 0.5*(96)<BR>\n" );
document.write( "area of hexagon = <font color=red>48 square centimeters</font>\r<BR>\n" );
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