Find the area of quadrilateral QUAD whose vertices are Q(-5, 5), U(4, 2), A(1, -3), and D (-3, -4).

Question

Find the area of quadrilateral QUAD whose vertices are Q(-5, 5), U(4, 2), A(1, -3), and D (-3, -4).

Answer 1

The area of a triangle given the co-ordinates of the vertices is

|x₁ y₁ 1|

det |x₂ y₂ 1|

|x₃ y₃ 1|

where the vertices are numbered counterclockwise.

Divide the quadrilateral into 2 triangles and evaluate the 2 determinants and add.

There is also a formula from Bramagupta which requires computation of the lengths of all the sides. Or if you know the lengths of the sides and of one diagonal, you can use Heron's formula for each of the two triangles.

It might be easier to get the areas of 3 right triangles which surround the given triangle and subtract the sum from the area of the rectangle which those 3 triangles make.

In any event no matter which method you choose it will be messy.