Area of a Triangle

• The area of a triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3), is given by

\Delta=\frac{1}{2}\begin{vmatrix}x_{1} & y_{1} & 1 \\x_{2} & y_{2} & 1 \\x_{3} & y_{3} & 1 \end{vmatrix}

• Since area is a positive quantity, we always take the absolute value of the determinant.
• If area is given, use both positive and negative values of the determinant for calculation.
• The area of the triangle formed by three collinear points is zero.

View the Topic in this video From 00:15 To 06:01

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1. The area of a triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3), is given by

\Delta=\frac{1}{2}\begin{vmatrix}x_{1} & y_{1} & 1 \\x_{2} & y_{2} & 1 \\x_{3} & y_{3} & 1 \end{vmatrix}