A "cross section" is what occurs when you "slice" a given shape in a particular way, so that you can visualise the shape in two parts (with 2 new faces). The cross section is the surface (face) of the side which you have just sliced.
E.g If you imagine a cone, with the circular base resting on a surface. You now slice the cone horizontally, so that you now have a very small cone (on top), and a "truncated cone" (2 circular faces, top one slightly smaller, with sloping sides joining them) below. The "cross section" is the top face of the truncated cone, and the lower face of the small cone (both cross sections are the same!). i.e they are the new "sides" that you have created. These new "faces" are both circular, so if you were to find the area you would use the formula pi*radius^squared = area.
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Average area
it means to do area
Messy area/area where pigs are kept
The area of a shape is measured in square units
The surface area is the sum of all the shapes' area