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 the equation s=ph+2b for the perimeter p of the base, we need to isolate p by itself on one side of the equation.
s = ph + 2b
To do this, we can subtract 2b from both sides of the equation:
s - 2b = ph
Next, we can divide both sides of the equation by h:
(s - 2b)/h = p
Now the equation is solved for the perimeter of the base:
p = (s - 2b)/h
B. To calculate the perimeter of the base of the rectangular prism, we need to plug in the given values for surface area s, base area b, and height h into the formula we derived in part A:
p = (s - 2b)/h
Plugging in the values:
p = (96 - 2(8))/4
p = (96 - 16)/4
p = 80/4
p = 20 meters
The perimeter of the base of the rectangular prism is 20 meters.