document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192605>Question 192605</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the area of an equilateral triangle with apothem 5.8cm? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144589 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=144589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> please  draw  sketch  of  equilateral  triangle\r<BR>\n" );
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document.write( "from  center  draw  lines  to  each  vertex.\r<BR>\n" );
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document.write( "now  sketch  apothem  as  altitude  to  center  from  mid  point  of  each  side\r<BR>\n" );
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document.write( "the  equilateral  triangle  now  has  3  equal  triangles  inside.  Each  of  these  is  divided  into  2  equal  triangles  by  the  apothem\r<BR>\n" );
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document.write( "the  central  angle  of  each  of  these  triangles  is  60 deg, the  angle  of  apothem  to  side  is  90 deg, and  the  other  angle  is  30.\r<BR>\n" );
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document.write( "this  makes  a  30-60-90  triangle,  with  small  leg  as  apothem =5.8 cm.\r<BR>\n" );
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document.write( "the  standard  proportions  of  the  30-60-90  makes  the  longer  leg = 5.8sqrt3.\r<BR>\n" );
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document.write( "this  longer  leg  is  1/2  of  a  side, therefore  side  =2*5.8sqrt3=11.6sqrt3=20.09\r<BR>\n" );
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document.write( "the  perimeter  of  base  equilateral  triangle  is  3* 20.09 or= 60.275\r<BR>\n" );
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document.write( "remember  for  any  polygon  area  =  1/2 * per* apothem=1/2*60.275*5.8=174.798\r<BR>\n" );
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document.write( "check  using  Heron's  formula<BR>\n" );
document.write( "sp=1/2 * 60.275  =30.1375<BR>\n" );
document.write( "30.1375-20.09=10.05<BR>\n" );
document.write( "A=sqrt( ( 30.1375)(10.05)^3)=174.84  ok </SPAN>\n" );
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