Answer:
We have, \[A(-4,8),\text{ }B(-3,-4),\text{ }C(0,-5)\] and \[D(5,6)\]are the vertices of a quadrilateral. Join A and C. Then, area of quadrilateral ABCD= (area of \[\Delta \,ABC\]) + (area of \[\Delta \,ACD\]) Area of \[\Delta \,ABC\] \[=\frac{1}{2}[-4(-4+5)-3(-5-8)+0(8+4)]\] \[=\frac{1}{2}[-4+39]=\frac{35}{2}\] sq. units And, area of \[\Delta \,ACD\] \[=\frac{1}{2}[-4(-5-6)+0(6-8)+5(8+5)]\] \[=\frac{1}{2}[44+65]\] \[=\frac{109}{2}\] sq. units \[\therefore \] Area of quadrilateral ABCD = Area of \[\Delta \text{ }ABC\] + Area of \[\Delta \text{ }ACD\] \[=\frac{35}{2}+\frac{109}{2}\] \[=\frac{144}{2}\] sq. units \[=72\] sq. units.
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