(Q10) If A(-5,7) , B(-4,-5) , C(-1,-6) and D(4,5) are the vertices of a quadrilateral then, find the area of quadrilateral ABCD.

By joining B to D , you will get two triangle ABD, and BCD. The area of ∆ABD

ABCD
=
1
2
 |5(--)+(-4)(-)+4(+)|
=
1
2
 || =
||
2
 = square units

Also, The area of ∆BCD

=
1
2
 |-4 (- -) -1 (+)+4(-+)|
=
1
2
 |-+| = 19 Sq units

So, the area of quadrilateral ABCD = Area of ∆ABD + Area of ∆BCD.

+ = square units.