document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148965>Question 1148965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABCD is a trapezoid with AD||BC (AD is parallel to BC). If AD=8cm and BC=14cm, and if the area of the trapezoid is 166cm^2, find the area of triangle ABE, in cm^2. \r<BR>\n" );
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document.write( "Diagram: https://imgur.com/a/4RzEFl1 </SPAN>\n" );
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document.write( "With AD parallel to BC and E the midpoint of CD, the area of triangle ABE is half the area of the trapezoid.<br><BR>\n" );
document.write( "ANSWER: The area of triangle ABE is 166/2 = 83 cm^2.<br><BR>\n" );
document.write( "To see that this is true, consider the midline EF of the trapezoid.<br><BR>\n" );
document.write( "Let the height of the trapezoid be 2x; then the altitudes of triangles ADE, AFE, BFE, and BEC are all x.<br><BR>\n" );
document.write( "The area of triangle ABE is the sum of the areas of triangles AFE and BFE:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2811%29%28x%29%2B%281%2F2%29%2811%29%28x%29+=+11x ALIGN=MIDDLE  ALT=\"%281%2F2%29%2811%29%28x%29%2B%281%2F2%29%2811%29%28x%29+=+11x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The area of the trapezoid is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%288%2B14%29%282x%29+=+22x ALIGN=MIDDLE  ALT=\"%281%2F2%29%288%2B14%29%282x%29+=+22x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the area of triangle ABE is half the area of the trapezoid.<br><BR>\n" );
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