Answer :

When the vertices of a quadrilateral is given then its area is given by {(x_{1}–x_{3})(y_{2}–y_{4}) – (x_{2}–x_{4})(y_{1}–y_{3})}

We must take all the vertices in counter clock wise direction otherwise it will give solution in negative.

So, from the figure we assume that

A (x_{1}, y_{1}) = (4, –1)

B (x_{2}, y_{2}) = (1, 2)

C (x_{3}, y_{3}) = (–3, 4)

D (x_{4}, y_{4}) = (–5, –6)

The area of the quadrilateral is {(x_{1}–x_{3})(y_{2}–y_{4}) – (x_{2}–x_{4})(y_{1}–y_{3})}

= {(4–(–3))(2–(–6)) –(–1–4)(1–(–5))}

= {56+30} = 43 Sq. units

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