# The area of quadrilateral whose vertices are (-5,7),(-4,-5),(-7,-6)and(4,5)isâ€‹

$\text { Area of triangle } ABC =\frac{1}{2}\left[ x _{1}\left( y _{2}- y _{3}\right)+ x _{2}\left( y _{3}- y _{1}\right)+ x _{3}\left( y _{1}- y _{2}\right)\right]$

$\\ Area \ of \ \ triangle \ A B C=\frac{1}{2}[-5(-5-(-6))+(-4)(-6-7)+(-1)(7-(-5))]\\ \begin{array}{l} =\frac{1}{2}[-5(-5+6)-4(-13)+(-1)(7+5)] \\ =\frac{1}{2}[-5(1)-4(-13)+(-1)(12)] \\ =\frac{1}{2}[-5+52-12] \\ =\frac{1}{2}[35] \text { square units } \end{array}$

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