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video example here

As you can see in the video, when extruding all the faces at once, they extrude along a normal that makes sense to me. However, when selecting only one of the faces, it extrudes in a weird direction which doesn't seem to match the direction the face is pointing in. The same thing happens to the face I try to extrude at the end. Why is this happening and how do I fix it?

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The difference is that when extruding a group of faces they are extruded along the averaged normal of all selected faces (no matter if they are connected or not) while extruding a single face only extrudes along the normal of the face since there are no others to be averaged with.

When you say the single face extrudes in a weird direction which does not seem to match the direction of the face, I guess with the direction you mean the slanted sides - but that's not the "direction" of the face. The direction or correctly the face normal is pointing outwards from the face orthogonally, i.e. in a right angle. And as you can see below that is not the angle which I think you have in mind (red the slanted sides, blue the face normal):

perceived angle vs. face normal

When you look at your video, while extruding along the face normals it shows the faces' Z direction (the normals) in blue, and they are orthogonal to the faces from which you extrude:

extruding laong face normals

So there is actually nothing to fix, because nothing is broken. One thing you can do is create a custom transform orientation, but this will only help in a limited way.

For example, let's say you want to extrude the single face in the same direction as the combined faces. The way you do it is the following: select all faces, then click on the Transform Orientation dropdown and there on the + button to create a new custom orientation from the selection (it will be called "Face" automatically).

custom transform orientation

If you now select a single face and hit E to extrude it, it seems nothing has changed because Blender assumes you want to extrude a single face on its local normal, so hit Z twice - the first time disables any axis locking, the second time now enables locking to Z on the custom axis.

extrude along custom normal

But depending on how the averaged normal is oriented, this might still not look correct for the single face. You could consider choosing a different face to base the custom transformation, for example one of the slanted side faces. In this case you would of course have to extrude along X or Y instead of Z. Extruding to the custom X axis would also require hitting the axis button X twice, first to change from face normal to face X, second to change to custom X axis.

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