document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117226>Question 1117226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a circle with diameter of 20 cm, a regular five-pointed star touching its circumference is inscribed.Find the area of the star.\r<BR>\n" );
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document.write( "Answer: 112.267 sq cm\r<BR>\n" );
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document.write( "Need solution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #732244 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=732244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 5 central angles<BR>\n" );
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document.write( "each angle is 360/5 = 72 degrees<BR>\n" );
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document.write( "label a point of the star on the circumference A, center of the circle O and the intersection of the side of A and the side of the point of the star adjacent to A going clockwise B.<BR>\n" );
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document.write( "angle AOB is 72/2 = 36 degrees and angle AOB is 36/2 = 18 degrees<BR>\n" );
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document.write( "for triangle AOB, we have<BR>\n" );
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document.write( "36 +18 +Beta = 180<BR>\n" );
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document.write( "Beta = 180 -36 -18 = 126 degrees<BR>\n" );
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document.write( "radius of circle = 20/2 = 10 cm<BR>\n" );
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document.write( "Now use the law of sines <BR>\n" );
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document.write( "(OB/sin(18)) = (10/sin(126))<BR>\n" );
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document.write( "OB = 10 * sin(18) / sin(126)<BR>\n" );
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document.write( "OB = 3.8197<BR>\n" );
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document.write( "Area of triangle AOB = (1/2) * 3.8197 * 10 * sin(36) = 11.2258<BR>\n" );
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document.write( "Area of the five pointed star = 10 * 11.2258 = 112.258 square cm's<BR>\n" );
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