document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1008228>Question 1008228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the are of an equilateral triangle of side a. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623990 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=623990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can look it up or you can derive it.\r<BR>\n" );
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document.write( "if you look it up, you will see that the area of an equilateral triangle = a^2 * sqrt(3) / 4.\r<BR>\n" );
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document.write( "you derive it by using pythagorus rule for right triangles and solve for h in terms of a.\r<BR>\n" );
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document.write( "you will get h = a * sqrt(3)/2\r<BR>\n" );
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document.write( "area of any triangle = 1/2 * b * h which then becomes area of equilateral triangle = 1/2 * a * a * sqrt(3) / 2 which then becomes area of equilateral triangle = a^2 * sqrt(3) / 4.\r<BR>\n" );
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document.write( "either way, you will get area of equilateral triangle = a^2 * sqrt(3) / 4.\r<BR>\n" );
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document.write( "for example, if you let a = 20, then the area should be equal to 20^2 * sqrt(3) / 4 which would be equal to 100 * sqrt(3)\r<BR>\n" );
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document.write( "the height, by pythagorus, would be equal to sqrt(20^2 - 10^2) = sqrt(400-100) = sqrt(300) = sqrt(100*3) = 10*sqrt(3).\r<BR>\n" );
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document.write( "you have a height of 10 * sqrt(3) and a base of 20 and a hypotenuse of 20.\r<BR>\n" );
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document.write( "area = 1/2 * base * height = 1/2 * 20 * 10 * sqrt(3) which is equal to 100 * sqrt(3).\r<BR>\n" );
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document.write( "it checks out, so the formula for area in terma of a must be correct.\r<BR>\n" );
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document.write( "area of equilateral triangle = a^2 * sqrt(3) / 4.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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