The surface area of a prism is modeled by the equation s=ph+2b, where s
is the surface area, p is the perimeter of the base, h is height of the prism, and b is the area of the base.
A. Solve the equation s=ph+2b for the perimeter p of the base.
B. A rectangular prism has a height of 4 meters, a surface area of 96 square meters, and a base area of 8 square meters. Calculate the perimeter of the base of the prism.
In your final answers, include all of your calculations.
A. To solve for the perimeter p of the base, we can isolate the term p by subtracting 2b from both sides and then dividing by h:
s - 2b = ph
p = (s - 2b) / h
B. We are given s = 96, b = 8, and h = 4. Using the formula from part A:
p = (96 - 2(8)) / 4
p = 20
Therefore, the perimeter of the base of the prism is 20 meters.
Calculation:
p = (96 - 2(8)) / 4
p = (96 -16) / 4
p = 80/4
p = 20