question_answer

Find the area of the quadrilateral, the coordinates of whose angular points taken in order are \[(1,1),\,(3,4),\,(5,-2)\] and \[(4,-7)\].

A)  \[20.5\]sq. units 

B)  41 sq. units

C)  82 sq. units   

D)  \[61.5\]sq. units

Correct Answer: A

Solution :

Let ABCD be a quadrilateral with vertices \[A(1,1),\,B(3,4),\,C(5,-2)\] and \[D(4,-7)\]                         Area of quadrilateral ABCD = Area of \[\Delta ABC+\]Area of \[\Delta ADC\] ... (i) Now, area of \[\Delta ABC\] \[=\frac{1}{2}|1(6)+3(-3)+5(-3)|=\frac{1}{2}\times 18=9\,sq.\]units Similarly, area of             \[\Delta ADC=\frac{1}{2}|1(-5)+4(-3)+5(8)|\] \[=\frac{1}{2}\times 23=11.5\] sq. units Hence, area of quadrilateral ABCD  \[=9+11.5=20.5\] sq. units