What is the difference between lateral area and total surface area? Your answer: ? Total surface area includes 1 base instead of 2 bases like lateral does ? Lateral includes all the faces while total only includes the bases ? Total surface area includes the base(s) and all the faces while lateral does not include the ? Lateral just includes B, the area of the base while total does not Clear answer Back Next
The Correct Answer and Explanation is:
The correct answer is: Total surface area includes the base(s) and all the faces while lateral does not include the [bases].
The fundamental difference between lateral area and total surface area lies in whether the area of the object’s base or bases is included in the calculation. Both are measures of the area covering the surface of a three dimensional shape, but they account for different parts of it.
Lateral area is the surface area of a 3D object excluding its top and bottom bases. A helpful way to visualize this is to think of the “sides” of the object. For a prism or a cylinder, the lateral area is the area of all the faces that are not the bases. Imagine a can of soup. The lateral area is the paper label that wraps around the curved side of the can. It does not include the circular metal top or the circular metal bottom. For a pyramid or a cone, the lateral area is the area of the slanted surfaces that rise to meet at the single point, or apex, excluding the flat bottom.
Total surface area, in contrast, is the sum of the areas of all surfaces of the 3D object. It is a complete measurement of the entire exterior. To calculate it, you must find the lateral area first and then add the area of the base or bases. Returning to the soup can example, the total surface area would be the area of the paper label (the lateral area) plus the area of the top metal lid and the bottom metal lid (the two bases).
In formulaic terms, the relationship is simple:
Total Surface Area = Lateral Area + Area of the Base(s)
For a shape with two bases like a prism or cylinder, the formula is: TSA = LA + 2B, where B is the area of one base.
For a shape with one base like a pyramid or cone, the formula is: TSA = LA + B.
