document.write( "Question 1124787: What is the area of an isosceles trapezoid, if the lengths of its bases are 16 cm and 30 cm and the diagonals are perpendicular to each other? \n" ); document.write( "

Algebra.Com's Answer #741355 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "Let A, B, C and D are the vertices of the trapezoid, so the trapezoid is ABCD.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let AB be the longer base of 30 cm and CD be the other base of 16 cm long.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let the point O be the intersection of diagonals.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the triangles  AOB,  BOC,  COD  and  AOD  are right angled triangles.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since the trapezoid ABCD has equal lateral sides, the triangle AOB is isosceles right angled triangle.\r\n" );
document.write( "\r\n" );
document.write( "Since it base AB is 30 cm long,  its sides (the legs)  AO and  BO  are   cm long.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Similarly, the triangle COD is isosceles right angled triangle.\r\n" );
document.write( "\r\n" );
document.write( "Since it base CD is 16 cm long,  its sides (the legs) CO and  DO  are   cm long.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now the areas of the triangles are\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    for triangle  AOB:    = 225 cm^2;\r\n" );
document.write( "\r\n" );
document.write( "    for triangle  COD:    =  64 cm^2;\r\n" );
document.write( "\r\n" );
document.write( "    for triangle  BOC:    = 120 cm^2;\r\n" );
document.write( "\r\n" );
document.write( "    for triangle  AOD:    = 120 cm^2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The total area of the trapezoid is the sum of areas of triangles  225 + 64 + 120 + 120 = 529 cm^2.\r\n" );
document.write( "

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

\n" );