Which formulas can be used to find the surface area of a right prism where [tex]$p$[/tex] is the perimeter of the base, [tex]$h$[/tex] is the height of the prism, [tex]$B A$[/tex] is the area of bases, and [tex]$L A$[/tex] is the lateral area?
Check all that apply.
A. [tex]$S A=B A+p h$[/tex]
B. [tex]$S A=p+\angle A$[/tex]
C. [tex]$S A=B A-L A$[/tex]
D. [tex]$S A=\frac{1}{2} B A+L A$[/tex]
Answer (1)
The surface area of a right prism is the sum of the lateral area and twice the area of the base.
The lateral area is the product of the perimeter of the base and the height of the prism.
The correct formula is S A = L A + 2 B A or S A = p h + 2 B A .
None of the provided options are correct. N o n e
Explanation
Analyze the surface area of a right prism. Let's analyze the formulas for the surface area of a right prism. We know that the surface area ( S A ) is the sum of the lateral area ( L A ) and the area of the two bases (2* B A ). The lateral area is the perimeter of the base ( p ) times the height of the prism ( h ). So, we have:
S A = L A + 2 B A
and
L A = p h
Therefore,
S A = p h + 2 B A
Evaluate the given options. Now, let's evaluate the given options:
Option A: S A = B A + p h . This is incorrect because it only includes one base area instead of two. It should be S A = 2 B A + p h .
Option B: S A = p + ∠ A . This option is incorrect because it includes the perimeter and an angle, which doesn't align with the surface area formula. Also, ∠ A is not defined in the problem.
Option C: S A = B A − L A . This is incorrect because it subtracts the lateral area from the base area, which is not the correct way to calculate the surface area. It should be S A = 2 B A + L A .
Option D: S A = 2 1 B A + L A . This is incorrect because it uses half of the base area instead of twice the base area. It should be S A = 2 B A + L A .
Conclusion Based on the analysis, none of the provided options are correct. The correct formula should be S A = 2 B A + p h or S A = 2 B A + L A .
Examples
Understanding the surface area of a prism is useful in many real-world scenarios. For example, if you're wrapping a gift that's shaped like a rectangular prism, knowing the surface area helps you determine how much wrapping paper you'll need. Similarly, if you're painting a pillar in the shape of a prism, calculating the surface area allows you to estimate the amount of paint required. These calculations ensure you have enough materials without unnecessary waste, saving both time and resources.
