document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=276192>Question 276192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of an equilateral triangle, with apothem 10 times the square root of 3. inches? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201327 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=201327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The apothem of an equilateral triangle divides the triangle into two 30-60-90 right triangles, where the apothem is the long leg of the triangle.\r<BR>\n" );
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document.write( "The sides of a 30-60-90 right triangle are in proportion <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{2}:\frac{\sqrt{3}}{2}:1\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 10\sqrt{3}\"> is 20 times greater than <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\sqrt{3}}{2}\">, therefore the other two sides must measure 10 and 20 inches.\r<BR>\n" );
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document.write( "The area of a right triangle is one-half of the product of the measures of the two legs.  For your problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{10\,\cdot\,10\sqrt{3}}{2}\">\r<BR>\n" );
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document.write( "But that is the area of only one-half of the equilateral triangle, so the total area you seek is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10\,\cdot\,10\sqrt{3}\ =\ 100\sqrt{3}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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