document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062886>Question 1062886</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A regular decagon is inscribed inside a circle. The perimeter of the decagon is 50 units.\r<BR>\n" );
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document.write( "A: What is the approximate measure of the radius (rounded to the nearest hundredth of a unit)?\r<BR>\n" );
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document.write( "B: What is the approximate area of the circle (rounded to the nearest whole square unit)?\r<BR>\n" );
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document.write( "Select only one answer each for parts A and B.\r<BR>\n" );
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document.write( "	A: 8.09<BR>\n" );
document.write( "	A: 2.63<BR>\n" );
document.write( "	A: 7.69<BR>\n" );
document.write( "	A: 4.25<BR>\n" );
document.write( "	B: 22<BR>\n" );
document.write( "	B: 186<BR>\n" );
document.write( "	B: 206<BR>\n" );
document.write( "	B: 57<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677897 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a 10 sided object is 50 units, so each side is 5 units.<BR>\n" );
document.write( "This divides the polygon into 10 isosceles triangles, each of which has a radius for the two equal sides.<BR>\n" );
document.write( "Half the length of a side is 2.5 units<BR>\n" );
document.write( "The central angle is 36 degrees, and it is 18 degrees for the triangle whose sides are the radius, half the side length and the apothem.  <BR>\n" );
document.write( "sin 18=2.5/radius (the hypotenuse)<BR>\n" );
document.write( "radius=2.5/sin 18=8.09 units. A<BR>\n" );
document.write( "The area will be pi*(8.09)^2, and that will be greater than 3*64 (192), so it has to be 206 for B.<BR>\n" );
document.write( "The actual answer is 205.61 rounding upward to 206. </SPAN>\n" );
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