Jenny has found the total surface area and the lateral surface area of a prism but she can't remember which is which. She got answers of 144in² and 304in² how would you distinguish which answer is lateral surface area and which is total surface area
To distinguish between the total surface area and the lateral surface area, you can use the following equation:
Total Surface Area = Lateral Surface Area + 2(base area)
Given that the two answers are 144in² and 304in², you can substitute these values into the equation to determine which one corresponds to the lateral surface area.
For example, let's assume that 144in² represents the total surface area:
144in² = Lateral Surface Area + 2(base area)
Since you know the total surface area and the base area, you can solve for the lateral surface area. However, if you get a negative value or an answer that does not make sense within the context of the problem, then you know that 144in² is not the total surface area.
Similarly, you can apply the same process assuming that 304in² represents the total surface area. However, this time substitute 304in² in the equation:
304in² = Lateral Surface Area + 2(base area)
Once again, solve for the lateral surface area using the given values and check if the obtained value is reasonable. If it is, then you can conclude that 304in² represents the total surface area.
By using this method of substitution and checking the reasonability of the results, you can distinguish which answer corresponds to the lateral surface area and which one represents the total surface area.