How to find area of quadrilateral in coordinate geometry
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What is the direct formula to find the area of quadrilateral in coordinate geometry ?
Asked by admin @ in Math viewed by 269 People
What is the direct formula to find the area of quadrilateral in coordinate geometry ?
Answered by admin @
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.
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