document.write( "Question 1210163: Solve for the area of the composite figure.
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\n" ); document.write( "If an isosceles trapezoid CDFG was added below, where the height was the same as the triangle above and the bases had a length of 12 and 24, then what is the area of the new composite figure?
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Algebra.Com's Answer #851429 by mccravyedwin(407)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The figure on the site is not to scale.  Here it is drawn to scale.\r\n" );
document.write( "I will assume a kite ABCD on the left, although I agree with \r\n" );
document.write( "greenestamps that nothing tells us that's the case.\r\n" );
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document.write( "Triangle DOA is a 45-45-90 triangle so. DO = AO = 6. Its area\r\n" );
document.write( "is \"expr%281%2F2%29%2Abase%2Aheight=DO%2AOA=expr%281%2F2%29%2A6%2A6=18\"\r\n" );
document.write( "Triangle BOA is congruent to triangle DOA so it also has area 18.\r\n" );
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document.write( "You may recognize triangle DOC as a 6-8-10 right triangle and see\r\n" );
document.write( "right off that OC=8.  If not, use the Pythagorean theorem,\r\n" );
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document.write( "\"OC+=+sqrt%28DC%5E2-DO%5E2%29+=+sqrt%2810%5E2-6%5E2%29=sqrt%28100-36%29=sqrt%2864%29=8\"\r\n" );
document.write( "Triangle DOC's area is \"expr%281%2F2%29%2Abase%2Aheight=expr%281%2F2%29%2ADO%2AOC=expr%281%2F2%29%2A6%2A8=24\"\r\n" );
document.write( "Triangle BOC is congruent to triangle DOC so it also has area 24. \r\n" );
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document.write( "So the area of kite ABCD is 18+18+24+24 = 84\r\n" );
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document.write( "Triangle BCE's height (the green line) is the same length as OC = 8.\r\n" );
document.write( "so its area is \"expr%281%2F2%29%2Abase%2Aheight=expr%281%2F2%29%2ACE%2A8=expr%281%2F2%29%2A12%2A8=48\"\r\n" );
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document.write( "So the kite's area plus triangle BCE's area is 48.\r\n" );
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document.write( "So the area of the composite figure is 84 + 48 = 132 square units.\r\n" );
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document.write( "For the other problem, they have added on an isosceles trapezoid on the right,\r\n" );
document.write( "I use different lettering, as they didn't put any lettering on the figures.\r\n" );
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document.write( "Let's draw in a couple of red lines and you will see what has been added:\r\n" );
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document.write( "Now you see that they have added on three more triangles all congruent to\r\n" );
document.write( "triangle BCE.  We found triangle BCE's area to be 48, so we just add (3)(48)=144\r\n" );
document.write( "to the area in the first problem, which was 132.\r\n" );
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document.write( "So the area of this new composite figure is 132+144 = 276 square units. \r\n" );
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document.write( "Edwin
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