# For a linear triangular element with (xi, yi) as the coordinates of the ith node of the element, which option denotes twice the Area of the triangle?

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For a linear triangular element with (xi, yi) as the coordinates of the ith node of the element, which option denotes twice the Area of the triangle?

(a) (x1y2 − x2y1) + (x2y3 − x3y2) + (x3y1 − x1y3)

(b) (x1y2 – x3y1) + (x2y3 – x1y2) + (x3y1 – x2y3)

(c) (x1y2 − x2y1) + (x2y3 − x3y2)

(d) (x1y1 − x2y2) + (x2y2 − x3y3) + (x3y3 − x1y1)

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I need to ask this question from Boundary Value Problems topic in division Single Variable Problems of Finite Element Method

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The correct choice is (a) (x1y2 − x2y1) + (x2y3 − x3y2) + (x3y1 − x1y3)

The best explanation: A linear triangular element has 3 nodes. With (xi, yi) as coordinates of i^th node, the twice of area is given by determinant of the matrix $\begin{pmatrix}1&x1&y1\\1&x2&y2\\1&x3&y3\end{pmatrix}$which equals to (x1y2 − x2y1) + (x2y3 − x3y2) + (x3y1 − x1y3).

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