document.write( "Question 268147: find the area of the convex polygon in the plane with vertices at the points whose coordinates are (-2,3), (1,10), (5,10) (8,7), and (4,0). \n" ); document.write( "

Algebra.Com's Answer #196623 by Edwin McCravy(20085) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Graph the points:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Get them in order going counter-clockwise around\r\n" );
document.write( "the polygon.  \r\n" );
document.write( "\r\n" );
document.write( "(-2,3), (4,0), (8,7) (5,10), and (1,10).\r\n" );
document.write( "\r\n" );
document.write( "Now we write the equation for the area in terms\r\n" );
document.write( "of the 6x2 \"determinant\" where each ordered pair of \r\n" );
document.write( "coordinates appear on each row in that counter-\r\n" );
document.write( "clockwise order, repeating the first ordered pair \r\n" );
document.write( "of coordinates at the bottom.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now to evaluate that \"determinant\" we \r\n" );
document.write( "\r\n" );
document.write( "Add the sum of the products of each x-coordinate \r\n" );
document.write( "by the y-coordinate of the point just below it,\r\n" );
document.write( "and then subtract the sum of the products of each \r\n" );
document.write( "y-coordinate by the x-coordinate of the point just \r\n" );
document.write( "below it.\r\n" );
document.write( "\r\n" );
document.write( "So we get\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );