document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1017819>Question 1017819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An exterior angle of a regular polygon measures 18 degrees. How many sides does the polygon have? If the length of the side of the polygon is 2 units, what is the area of the polygon? There are 20 sides just need help on the last part.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634062 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=634062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 20 sides to the polygon.<BR>\n" );
document.write( "each side measures 2 units.\r<BR>\n" );
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document.write( "the polygon is divided into 20 isosceles triangles with the base of each isosceles triangle equal to 2.\r<BR>\n" );
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document.write( "the central angle each of the isosceles triangles is the same as the external angle of the polygon which is 18 degrees.\r<BR>\n" );
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document.write( "the other two angles of the isosceles triangle are therefore equal to (180 - 18) / 2 = 162 / 2 = 81 degrees each.\r<BR>\n" );
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document.write( "this is because the sum of the angles of any triangle is equal to 180.\r<BR>\n" );
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document.write( "18 + 2 * 81 = 18 + 162 = 180.\r<BR>\n" );
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document.write( "if you know the formula for the area of an isosceles triangle, you can simply work from there.\r<BR>\n" );
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document.write( "if not, then you need to solve for the altitude of the triangle and then find the area.\r<BR>\n" );
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document.write( "we'll assume we don't know it and we'll solve for the altitude.\r<BR>\n" );
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document.write( "since the base is 2 and the central angle of the triangle is 18, we can divide the isosceles triangle into 2 right triangles with base of 1 and angle of 9.\r<BR>\n" );
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document.write( "the altitude for this triangle would be tan(9) = 1/x, where x is the altitude.\r<BR>\n" );
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document.write( "solve for x to get x = 1/tan(9) = 6.313751515.\r<BR>\n" );
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document.write( "the areaa of the isosceles triangle is equal to 1/2 * b * h which is equal to 1/2 * 2 * 6.313751515 which is equal to 6.313751515.\r<BR>\n" );
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document.write( "since there are 20 of these isosceles triangles that make up the area of the polygon, then the area of the polygon is 20 * 6.313751515 = 126.2750503 square units.\r<BR>\n" );
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document.write( "i verified with an online calculator that this result is accurate.\r<BR>\n" );
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document.write( "a picture of your polygon is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/020401.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "a picture of one of the twenty isosceles triangles is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/020402.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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