document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208996>Question 1208996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABCD is a trapezoid in which AD: BC=3:5. If the area of<BR>\n" );
document.write( "triangle AMD is 315 cm2, find the area of the trapezoid is, in cm2.<BR>\n" );
document.write( "https://ibb.co/HTrxtP9 </SPAN>\n" );
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document.write( "Answer: <font color=red>2240 square cm</font>\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-4%2C4.14%2C-4%2C3%2C%0D%0Aline%28-2%2C2%2C2%2C2%29%2Cline%282%2C2%2C3.14%2C-2.98%29%2Cline%283.14%2C-2.98%2C-3%2C-3%29%2Cline%28-3%2C-3%2C-2%2C2%29%2Cline%28-2%2C2%2C3.14%2C-2.98%29%2Cline%282%2C2%2C-3%2C-3%29%2C%0D%0Alocate%28-2.5%2C2%2C%22A%22%29%2Clocate%28-3%2C-3%2C%22B%22%29%2Clocate%283.14%2C-2.98%2C%22C%22%29%2Clocate%282.3%2C2%2C%22D%22%29%2Clocate%280.0316205534-0.5%2C0.0316205534%2C%22M%22%29%2C%0D%0Aline%28-2%2C2%2C0.64%2C2%29%2Cline%280.64%2C2%2C0.4114%2C1.868%29%2Cline%280.64%2C2%2C0.4114%2C2.132%29%2Cline%28-3%2C-3%2C0.3800292838%2C-2.9889901326%29%2Cline%280.3800292838%2C-2.9889901326%2C0.0878292838%2C-3.1589901326%29%2Cline%280.3800292838%2C-2.9889901326%2C0.0867292838%2C-2.8209901326%29%2C%0D%0Alocate%28-3.5%2C-3.5%2Cmatrix%281%2C4%2C%22Diagram%22%2C%22not%22%2C%22to%22%2C%22scale%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "AD is parallel to BC due to the arrow markers.\r<BR>\n" );
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document.write( "These parallel segments allow us to determine these two facts:<BR>\n" );
document.write( "angle ADB = angle DBC<BR>\n" );
document.write( "angle DAC = angle BCA<BR>\n" );
document.write( "The reason for each is the Alternate Interior Angle Theorem.\r<BR>\n" );
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document.write( "We can then use the Angle Angle Theorem to prove triangle AMD is similar to triangle CMB.\r<BR>\n" );
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document.write( "Segments AD and BC are in ratio 3:5<BR>\n" );
document.write( "That scales up to 3x:5x<BR>\n" );
document.write( "AD = 3x<BR>\n" );
document.write( "BC = 5x<BR>\n" );
document.write( "where x is some positive real number.\r<BR>\n" );
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document.write( "Rephrased another way: AD = (3/5)*BC = 0.6BC\r<BR>\n" );
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document.write( "Let h be the height of triangle CMB<BR>\n" );
document.write( "(3/5)h = 0.6h is the height of triangle AMD because the triangles are similar.\r<BR>\n" );
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document.write( "area of triangle = 0.5*base*height<BR>\n" );
document.write( "areaAMD = 0.5*AD*0.6h<BR>\n" );
document.write( "areaAMD = 0.5*3x*0.6h<BR>\n" );
document.write( "areaAMD = 0.9x*h<BR>\n" );
document.write( "0.9x*h = 315<BR>\n" );
document.write( "x*h = 315/0.9<BR>\n" );
document.write( "<font color=blue>x*h = 350</font><BR>\n" );
document.write( "Let's call this <font color=blue>equation (1)</font> to use later.\r<BR>\n" );
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document.write( "Since h and 0.6h are the heights of triangles CMB and AMD respectively, this means the height of the trapezoid is h+0.6h = 1.6h\r<BR>\n" );
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document.write( "area of trapezoid = 0.5*height*(base1+base2)<BR>\n" );
document.write( "areaABCD = 0.5*1.6h*(AD+BC)<BR>\n" );
document.write( "areaABCD = 0.5*1.6h*(3x+5x)<BR>\n" );
document.write( "areaABCD = 0.5*1.6h*(8x)<BR>\n" );
document.write( "areaABCD = 0.5*1.6*8*(<font color=blue>x*h</font>)<BR>\n" );
document.write( "areaABCD = 0.5*1.6*8*(<font color=blue>350</font>) ........ applying <font color=blue>equation (1)</font><BR>\n" );
document.write( "areaABCD = <font color=red>2240 square cm</font>\r<BR>\n" );
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document.write( "I used <a  rel=nofollow HREF=\"https://www.geogebra.org/calculator\">GeoGebra</a> to confirm the answer is correct.\r<BR>\n" );
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document.write( "A similar question is found <a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.1148964.html\">here</a><BR>\n" );
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