document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=310745>Question 310745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the area of an equilateral triangle with an apothem having a length of 4 feet. round to the nearest tenth </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #222235 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=222235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The apothem of an equilateral triangle forms a 30-60-90 right triangle where the apothem is the long leg, one side of the triangle is the hypotenuse, and one-half of the side is the short leg.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "With a tip o'the hat to Mr. Pythagoras, letting <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the measure of the hypotenuse, we can say:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ =\ \left(\frac{x}{2}\right)^2\ +\ 16\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And a little algebra and rationalizing the denominator gets us to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{8\sqrt{3}}{3}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence the measure of the short side of the triangle is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x}{2}\ =\ \frac{4\sqrt{3}}{3}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The 30-60-90 triangle is one-half of the equilateral triangle, so:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ 2\left(\frac{4\,\cdot\,\frac{4\sqrt{3}}{3}}{2}\right)\ =\ \frac{4\,\cdot\,4\sqrt{3}}{3}\ =\ \frac{16\sqrt{3}}{3}\ \approx\ 9.2\"> feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );