Question

What is the direct formula to find the area of quadrilateral in coordinate geometry ?

Answer 1

Answer:

If the vertices are at

( x₀, y₀ ), ( x₁, y₁ ), ( x₂, y₂ ), ( x₃, y₃ )

then the (signed) area is

(1/2) × ( x₀y₁ - x₁y₀ + x₁y₂ - x₂y₁ + x₂y₃ - x₃y₂ + x₃y₀ - x₀y₃ ).

For the "normal" area, just ignore the sign if you get a negative value.

This can be extended to polygons with any number of sides, just keep going with the same pattern.

An illustration of its use in GeoGebra is attached.

Answer 2

divide the quadrilateral into two by making a diagonal

Now, you have 2 triangles.

Now use the formula of area of triangle