Let's clarify the difference between lateral and total surface area of a prism. It's a common point of confusion, but with a clear explanation, it becomes quite straightforward.
The lateral surface area (LSA) of a prism is the sum of the areas of all its lateral faces, excluding the bases. Think of it as the area of all the sides of the prism, without the top and bottom.
The total surface area (TSA) of a prism is the sum of the areas of all its faces, including the bases. It's the entire surface area you would need to cover if you were wrapping the prism.
| Feature | Lateral Surface Area (LSA) | Total Surface Area (TSA) |
|---|---|---|
| Definition | Area of all faces excluding bases | Area of all faces including bases |
| Faces Included | Lateral faces only | Lateral faces and bases |
| Formula | $LSA = Ph$ (where P is the perimeter of the base and h is the height of the prism) | $TSA = LSA + 2B$ (where B is the area of the base) |
| Application | Calculating the area to paint the sides of a prism-shaped object | Calculating the area to wrap the entire prism-shaped object |
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