Calculate the area of the quadrilateral formed with the vertices (-3,2),(5,4),(7,-6) and (-5,-4).

80 square units

Area of the quadrilateral

= \(\frac{1}{2}\) × [ ( a1.b2 + a2.b3 + a3.b4 + a4.b1 ) - ( a2.b1 + a3.b2 + a4b3 + a1.b4 ) ]

Four points of quadrilateral = (-3,2) , (5,4) , (7,-6) and (-5,-4)

= \(\frac{1}{2}\) × [ ( -3×4 + 5×(-6)  + 7×(-4) + (-5)×2 ) - ( 5×2 + 7×4 + (-5)×(-6) + (-3)×(-4)   ) ] 

= \(\frac{1}{2}\) × [ ( -12 -30 -28 -10 ) - (10 + 28 + 30 + 12   ) ]

= \(\frac{1}{2}\) × [ - 80  - 80 ]

= - 80

[ Area can't be negative ]

= 80 square units