Find triangle area from three vertices on the coordinate plane
Result
Triangle Area
Step-by-Step Derivation
Triangle Area Coordinate Formula
A = |x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)| / 2
The coordinate triangle area formula is a determinant version of the shoelace method. It uses vertex coordinates directly, so no side lengths, heights, or angles are required.
⚠If the computed area is 0, the three points are collinear and no nonzero triangle is formed.
How Coordinate Triangle Area Works
The determinant measures the signed area created by the three points. Taking the absolute value gives the actual geometric area.
Three Vertices
Use the coordinates of all triangle corners.
Determinant
The formula measures signed area.
Absolute Value
Area is always nonnegative.
Collinearity
Zero area means points lie on one line.
💡 Example: For (0,0), (4,0), (0,3), area = 6.
Applications of Coordinate Triangle Area
Coordinate GeometrySurveyingComputer GraphicsPolygon Area
Frequently Asked Questions
What is a triangle area coordinate calculator?▼
It finds the area of a triangle from three coordinate points.
What is the coordinate triangle area formula?▼
Area = |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|/2.
How do I use this calculator?▼
Enter the coordinates of three vertices and click Calculate.
What if the area is zero?▼
Area zero means the three points are collinear and do not form a triangle.
Where is coordinate triangle area used?▼
It is used in coordinate geometry, surveying, graphics, and polygon area calculations.
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