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Jacobian for 6-noded triangle in 3D to calculate the area

Assuming an isoparametric formulation and using the shape functions you show in your post, you can write $x=N_ix_i, y=N_iy_i$, and $x=N_iz_i$ where $x_i, y_i$, and $z_i$ are the coordinates of the six ...
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