document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166971>Question 1166971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the diagram, O is the centre of the circle and sector angle COB is 120 degrees. CB has arc length 4 π cm. Also AC=AB. Find the area, in cm*2, of the shaded region.<BR>\n" );
document.write( "A)30<BR>\n" );
document.write( "B)18 √ 3<BR>\n" );
document.write( "C) 27 √ 3<BR>\n" );
document.write( "D) 27<BR>\n" );
document.write( "E) 24 √ 3\r<BR>\n" );
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document.write( "https://imageshack.com/i/pn2akcrPj<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791536 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the diagram, O is the centre of the circle and sector angle COB is 120 degrees.<BR>\n" );
document.write( " CB has arc length 4 π cm.<BR>\n" );
document.write( " Also AC=AB. Find the area, in cm*2, of the shaded region.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the radius, the given arc = 4<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > and is 1/3 the circumference therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Ar+=+12pi ALIGN=MIDDLE  ALT=\"2pi%2Ar+=+12pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by pi<BR>\n" );
document.write( "2r = 12<BR>\n" );
document.write( "r = 6 cm is the radius<BR>\n" );
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document.write( "draw the radius from A to 0 which gives us two equal isosceles triangles<BR>\n" );
document.write( "Each of these triangle can be divided into two right triangles with angles of 60 degrees at the center.<BR>\n" );
document.write( "The hypotenuse of these triangles is the radius, 6 cm<BR>\n" );
document.write( "Find the other two side of the right triangles using sine and cosine of 60 degrees.<BR>\n" );
document.write( "sin(60) = s1/6<BR>\n" );
document.write( "s1 = 5.196 cm<BR>\n" );
document.write( "cos(60) = s2/6<BR>\n" );
document.write( "s2 = 3 cm<BR>\n" );
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document.write( "Find the area of one of the right triangles<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >5.196 * 3<BR>\n" );
document.write( "A = 7.794 sq/cm<BR>\n" );
document.write( "The shaded are consist of 4 right triangle, therefore<BR>\n" );
document.write( "4 * 7.794 = 31.176 sq/cm is the shaded area which is B <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2818%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%2818%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( " <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );