Jenny has found the total surface area of the lateral surface area of a prism but she can't remember which it is she got answers of 144-in square and 304 in square how would you distinguish which answer is lateral surface area of which is total surface area
To distinguish which answer is the lateral surface area (LSA) and which is the total surface area (TSA), we can look at the formulas for each:
1. Lateral Surface Area (LSA) is the sum of the areas of all the lateral faces of the prism. It does not include the bases.
LSA = perimeter of base × height of prism
2. Total Surface Area (TSA) is the sum of the areas of all the faces of the prism, including the bases.
TSA = LSA + 2(base area)
Now, let's analyze the given answers of 144 in square and 304 in square:
1. 144 in square: This could be the LSA since it is smaller. If Jenny's calculation is correct, it means she only considered the lateral faces and not the bases. Therefore, 144 in square is likely the LSA.
2. 304 in square: This could be the TSA since it is larger. If Jenny's calculation is correct, it means she included the bases in her calculation. Therefore, 304 in square is likely the TSA.
By comparing the relative sizes of the two values and considering the definitions of LSA and TSA, we can determine which answer corresponds to each surface area.