document.write( "Question 1208983: A triangle with sides of 21 cm, 72 cm and 75 cm is cut into parts that form a quadrilateral. Find, in cm2, the area of the largest quadrilateral that can be formed.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #847532 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A triangle with sides of 21 cm, 72 cm and 75 cm is cut into parts that form a quadrilateral.
\n" ); document.write( "Find, in cm2, the area of the largest quadrilateral that can be formed.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "In this problem, it is assumed that the quadrilateral is formed of disjoint parts\r\n" );
document.write( "of the triangle with no holes (empty spaces) and without overlaying.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the area of the quadrilateral is equal to the area of the original triangle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The area of the original triangle can be found using the Heron's formula\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    S = ,  where s is the semi-perimeter  s =  = 84 cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, for the area we have\r\n" );
document.write( "\r\n" );
document.write( "    S =  =  = 756 cm^2.    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "By the way, it is easy to check that the triangle with the sides\r
\n" ); document.write( "\n" ); document.write( "21 cm, 72 cm and 75 cm is a right-angled triangle.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So, it gives another, more simple way to calculate its area $\"%281%2F2%29%2A21%2A72\"$ = 756 cm^2.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );