# For a linear triangular element with (xi, yi) as the coordinates of the i^th node of the element the area=10units, the value of ∑αi from the standard relation αi+βiX+γiY=(2/3)*Area where X=∑xi, Y=∑yi is ___

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For a linear triangular element with (xi, yi) as the coordinates of the i^th node of the element the area=10units, the value of ∑αi from the standard relation αi+βiX+γiY=(2/3)*Area where X=∑xi, Y=∑yi is ___

(a) 10

(b) 20

(c) 30

(d) 40

This question was addressed to me at a job interview.

My query is from Boundary Value Problems topic in division Single Variable Problems of Finite Element Method

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Correct option is (b) 20

To elaborate: A linear triangular element has 3 nodes. With (xi, yi) as coordinates of ith 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). Then from the standard relation we have ∑αi = (x2y3 − x3y2) + (x3y1 − x1y3) + (x1y2 − x2y1)

=2*Area

=2*10

=20.

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