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I've created these 2 objects and want to create a new object that represents the area where they intersect. I'm really confused as to why I cannot do it. I practiced on a cube and a cylinder in a new file and it work as expected. How do I find the issue with these objects? enter image description here

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You have doubles , flipped normals and ngons in your meshes.

Select the object named mask, enter edit mode and do the following :

-select all vertices , press w and remove doubles.
-recalculate normals with ctrln

result :

enter image description here

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