Find the area of the quadrilateral whose vertices are

(-4, 5), (0, 7), (5, -5), and (-4, -2)

Given (-4, 5), (0, 7), (5, -5), and (-4, -2)

To Find: Find the area of quadrilateral.

Let us Assume A(x₁, y₁) = (-4, 5)

Let us Assume B(x₂, y₂) = (0, 7)

Let us Assume C(x₃, y₃) = (5, -5)

Let us Assume D(x₄, y₄) = (4, -2)

Let us join Ac to from two triangles ∆ABC and ∆ACD

Now

Area of triangle

Then,

Area of given triangle ABC

Area of given triangle ABC

square units

Area of quadrilateral ABCD = Area of ABC + Area of ACD

Hence, Area of Quadrilateral ABCD sq units.