# u=u[x(e,n),y(e,n)] and v=v[x(e,n),y(e,n)] Using the chain rule of partial derivatives, we get Jacobian of the transformation, J. The relation between area (A) of 2D three noded triangular element and Jacobian is given by _____

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u=u[x(e,n),y(e,n)] and v=v[x(e,n),y(e,n)] Using the chain rule of partial derivatives, we get Jacobian of the transformation, J. The relation between area (A) of 2D three noded triangular element and Jacobian is given by _____

(a) A=1*&vert;detJ&vert;

(b) A=(1/3)*&vert;detJ&vert;

(c) A=0.5*&vert;detJ&vert;

(d) A=2*&vert;detJ&vert;

The question was posed to me during an internship interview.

I want to ask this question from Boundary Value Problems in chapter Single Variable Problems of Finite Element Method

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The correct answer is (c) A=0.5*&vert;detJ&vert;

Easy explanation: For a 2D three noded triangular element area A=(0.5)*&vert;(x1-x3)*(y2-y3)-(x2-x3)*(y1-y3)&vert;. Using the chain rule of partial derivatives, we get Jacobian of the transformation, J=$\begin{pmatrix}x1-x3&x2-x3\\y1-y3&y2-y3\end{pmatrix}$. Then detJ=(x1-x3)*(y2-y3)-(x2-x3)*(y1-y3) and in terms of detJ

A=A=0.5*&vert;detJ&vert;

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