Find the area of the quadrilateral whose vertices are

(1, 1), (7, -3), (12, 2) and (7, 21)

Given (1, 1), (7, -3), (12, 2) and (7, 21)

Let us Assume A(x₁, y₁) = (1, 1)

Let us Assume B(x₂, y₂) = (7, -3)

Let us Assume C(x₃, y₃) = (12, 2)

Let us Assume D(x₄, y₄) = (7, 21)

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

Now

Area of triangle

Then,

Area of given triangle ABC

= 25 square units

Area of given triangle ABC

= 107 square units

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

= 25 + 107

= 132 sq units.