Answer:
46 sq, units.
Step-by-step explanation:
Let the quadrilateral has vertices A(-4,-2), B(2,-4), C(6,2) and D(-6,2).
Let us draw a diagonal AC connecting vertices A and C.
Now, Area of ABCD = Area of Δ ABC + Area of Δ ACD
Now, area of Δ ABC is given by
[tex]\frac{1}{2} |- 4(- 4 - 2) + 2(2 - (- 2)) + 6( -2 - (-4))| = 22[/tex] sq. units.
Again, the area of Δ ACD is given by
[tex]\frac{1}{2} |- 4 (2 - 2) + 6(2 - (- 2)) - 6(- 2 - 2) | = 24[/tex] sq. unirs.
Therefore the are of the quadrilateral is = 22 + 24 = 46 sq. units. (Answer)
If ([tex]x_{1},y_{1}[/tex]), ([tex]x_{2},y_{2}[/tex]), and ([tex]x_{3},y_{3}[/tex]) are the three vertices of a triangle then the area of the triangle is given by
[tex]\frac{1}{2} |x_{1}(y_{2} - y_{3}) + x_{2}(y_{3} - y_{1}) + x_{3}(y_{1} - y_{2}) |[/tex] sq. units.
