Question 111606
given:

 vertices at ({{{1}}},{{{1}}}),({{{5}}},{{{2}}}),({{{4}}},{{{4}}}) and ({{{2}}},{{{3}}})

find: the area of the quadrilateral 


If 
({{{x[1]}}},{{{y[1]}}}; 
{{{x[2]}}},{{{y2}}});
{{{x[3]}}},{{{y[3]}}};
{{{x[4]}}},{{{y[4]}}}

 are the vertexes of the quadrilateral, the {{{area}}} is calculated from the formula :

{{{Area = 1/2 * ((x[1]-x[3])(y[2]-y[4]) - (x[2]-x[4])(y[1]-y[3]))}}}



= {{{(1/2)*((1*-4)(2*-3) -(5-2)(1-4))}}}



 = {{{(1/2) * ((4)(-6) -(3)(-3))}}}

= {{{(1/2)(-24-(-9))sq_units}}} 

={{{(1/2) ( -24 +9) sq_units}}}

={{{(1/2) ( -15) sq_units}}}

={{{( -15/2) sq_units}}}

={{{-(7.5) sq_units}}}