document.write( "Question 1195835: The trapezoid shown is divided into four triangles by its diagonals. The area of two triangles are indicated(9 and 25). What is the area of the whole trapezoid?
\n" ); document.write( "

\r
\n" );
document.write( "\n" );
document.write( "Note: Image may not be proportional \n" );
document.write( "
Algebra.Com's Answer #828402 by ikleyn(52847)  
You can put this solution on YOUR website!
 .
\n" );
document.write( "\r\n" );
document.write( "Let \"a\" be the shorter base of the trapezoid;\r\n" );
document.write( "\r\n" );
document.write( "let \"b\" be the longer base of the trapezoid.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The triangles of the areas 9 and 25 square units are similar, \r\n" );
document.write( "with the similarity coefficient of  (smaller to larger).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let h be the height of the smaller triangle drawn to its base \"a\";\r\n" );
document.write( "\r\n" );
document.write( "Let H be the height of the larger triangle drawn to its base \"b\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then from the similarity of triangles,  b = ;  H = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We have then   =  =  = ;\r\n" );
document.write( "\r\n" );
document.write( "              h + H =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The area of the trapezoid is  \r\n" );
document.write( "\r\n" );
document.write( "    Area =  =  = ;\r\n" );
document.write( "\r\n" );
document.write( "    but   = the area of the upper triangle = 9;  hence  ah = 2*9;  therefore\r\n" );
document.write( "\r\n" );
document.write( "    Area =  = 32*2 = 64 square units.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The area of the trapezoid is 64 square units.\r\n" );
document.write( "

\n" );
document.write( "Solved.
\n" );
document.write( " \n" );
document.write( "\n" );