Find the area of the quadrilateral whose vertices are

(–3, 4), (–5, – 6), (4, – 1) and (1, 2)

When the vertices of a quadrilateral is given then its area is given by {(x₁–x₃)(y₂–y₄) – (x₂–x₄)(y₁–y₃)}

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 (x₁, y₁) = (4, –1)

B (x₂, y₂) = (1, 2)

C (x₃, y₃) = (–3, 4)

D (x₄, y₄) = (–5, –6)

The area of the quadrilateral is {(x₁–x₃)(y₂–y₄) – (x₂–x₄)(y₁–y₃)}

= {(4–(–3))(2–(–6)) –(–1–4)(1–(–5))}

= {56+30} = 43 Sq. units