I guess so. "Shape" does not have that precise a definition.
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To find the the area of a shape is to find the space that is enclosed within a 2D object. Do not mix it up with volume, which is the space enclosed within a 3D object.
A 2D shape is flat and only has a surface area whereas a 3D shape is an object that has surface area and volume.
Paper is a 3D object.
A Sphere is an the name for a shape of a 3D object that is like a ball or a globe. If the shape is 2D then it is a circle
The cross section, of a 3D object, is the 2D shape made when a 2D plane cuts across the 3D object. Often "cross section" refers to the shape made when the plane is at right angles to an axis of the 3D object but this need not be the case.