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Total surface area is the area of the whole surface of any object including the area of base and the area of the top.
lateral surface area or curved surface area is the area of the object excluding the areas of base and the top. Fro eg. 
TSA of cuboid is = 2(lb+bh+lh) and the CSA of cuboid is = 2(l+b)h
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TSA area means the whole area and LSA means curved surface area