Geometry

Triangle Area (coordinates)

Area of a triangle from three vertices (shoelace).

Formula

Formula
A = ½x1(y2−y3)+x2(y3−y1)+x3(y1−y2)

Variables

SymbolDefinitionType & rangeUnitsRole
(xᵢ,yᵢ) three vertices computed result result

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Result

Worked examples

Example 1
Givenx₁ = 0, y₁ = 0, x₂ = 4, y₂ = 0, x₃ = 0, y₃ = 3
Result6
Example 2
Givenx₁ = 1, y₁ = 1, x₂ = 5, y₂ = 1, x₃ = 3, y₃ = 4
Result6