Answer:
We have \[P(-5,-3),Q(-4,-6),R(2,-3)\]and \[S(1,2)\] are the vertices of a quadrilateral PQRS. Join P and R. Then, Area of quad PQRS = (Area of \[\Delta \text{ }PQR\]) + (Area of\[\Delta \,PRS\]) Area of \[\Delta \text{ }PQR\] \[=\frac{1}{2}|-5(-6+3)-4(-3+3)+2(-3+6)|\] \[=\frac{1}{2}|-5(-3)-4(0)+2(3)|\] =\[\frac{1}{2}|15+6|=\frac{21}{2}\] sq. units And, area of \[\Delta \text{ }PRS\] \[=\frac{1}{2}|-5(-3-2)+2(2+3)+1(-3+3)|\] \[=\frac{1}{2}=|-5(-5)+2(5)+1(0)|\] \[=\frac{1}{2}|25+10|=\frac{35}{2}\] sq. units Hence, area of quad. \[PQRS=\text{Area of }\Delta \text{ }PQR+\text{Area of }\Delta \text{ }PRS\] \[=\left( \frac{21}{2}+\frac{35}{2} \right)\] sq. units \[=\frac{56}{2}\] sq. units \[=28\] sq. units
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