# Area of a 3-D triangle in terms of its projections on 3 Cartesian planes?

Geometry Level pending

Suppose a triangle $$ABC$$ with points $$A(x_1, y_1, z_1)$$, $$B(x_2,y_2,z_2)$$ and $$C(x_3,y_3,z_3)$$. Projection of this $$\triangle ABC$$ on $$xy$$-plane is of area $$A_1$$. Projection on $$yx$$-plane is of area $$A_2$$ and projection at $$zx$$-plane is of area $$A_3$$. What is the area of $$\triangle ABC$$ in terms of $$A_1$$, $$A_2$$, and $$A_3$$?

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