document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166927>Question 1166927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the triangle to the right, segments AB and AC are trisected, and D is the midpoint of BC. If the area of triangle ABC is 630 cm*2, then the area of the section marked x, in cm*2 is:<BR>\n" );
document.write( "A) 105<BR>\n" );
document.write( "B) 175<BR>\n" );
document.write( "C) 150<BR>\n" );
document.write( "D) 185<BR>\n" );
document.write( "E) 170\r<BR>\n" );
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document.write( "https://imageshack.com/i/pnLdNNl3j </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791487 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791487\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The two horizontal segments divide triangle ABC into a small triangle, a small trapezoid, and a larger trapezoid.  The heights of all three figures are the same.<br><BR>\n" );
document.write( "Segment BC and the two horizontal segments can also be viewed as forming three similar triangles all with vertex A; the ratio of the heights of those three triangles is 1:2:3.<br><BR>\n" );
document.write( "That means the height of the smallest triangle is 1/3 the height of triangle ABC, so the area of the smallest triangle is 1/9 of the area of triangle ABC.<br><BR>\n" );
document.write( "Similarly, the height of the middle sized triangle is 2/3 the height of triangle ABC, so the area of the middle sized triangle is 4/9 of the area of triangle ABC.<br><BR>\n" );
document.write( "That means the area of the larger trapezoid is 5/9 of the area of triangle ABC.<br><BR>\n" );
document.write( "Finally, since D is the midpoint of BC, segment AD bisects that larger trapezoid, so the area of the figure marked x is 5/18 of the area of triangle ABC.<br><BR>\n" );
document.write( "ANSWER: (5/18)*630 = 5*35 = 175 square cm<br><BR>\n" );
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