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Surface normals

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OK I want to calculate the vertex normals on my hexagonal terrain using a height map. I think that in order to do this, i need to calculate the surface normal of each of the 6 triangles that a vertex touches and then average their normals to create an average vertex normal, where the 6 triangles meet. I may be wrong in my method here, i am new to this. If anyone has a better idea, please tell me. Also how do i find a surface normal in, im sure there must be some kind of built in function for this. Thanx in advance!

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If you would have a square-based terrain, the equation would look like this:
(this is the average of the normals of the triangles that contain the point. Surprisingly simple.)
The hexagonal thing should be really similar, but not axis-aligned.

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