document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=547465>Question 547465</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the area of an equilateral triangle if I am only given the height?  The height (in this case) is 16.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank  you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356389 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=356389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given it is an equilateral triangle, then a line bisecting any vertex will bisect the opposite side.<BR>\n" );
document.write( "This will create two congruent triangles, each of which will be a 30-60-90 triangle.  <BR>\n" );
document.write( "Recall an equilateral triangle has 3 60-degree angles.<BR>\n" );
document.write( "The sides of a 30-60-90 triangle are known to have specific relationships.<BR>\n" );
document.write( "The hypotenuse = 2 * the short side, which = 1/2 the base in this case.<BR>\n" );
document.write( "The altitude = sqrt(3) * the short side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We are told the height (altitude) = 16, so.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "sqrt(3)*b/2 = 16<BR>\n" );
document.write( ".<BR>\n" );
document.write( "b = 32/sqrt(3)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "b = 18.47520861406803.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Check using the Pythagorean theorem.<BR>\n" );
document.write( "b/2 = 9.237604307034013<BR>\n" );
document.write( "(b/2)^2 = 85.33333333333336<BR>\n" );
document.write( "a^2 = 256<BR>\n" );
document.write( "c = sqrt(85.33333333333336+256)<BR>\n" );
document.write( "c = 18.47520861406803<BR>\n" );
document.write( "So, the hypotenuse = 18.47520861406803, which = the base.<BR>\n" );
document.write( "Recall, it is an equilateral triangle, so this makes perfect sense.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Done. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );