The surface area of a prism is modeled by the equation
S
=
P
h
+
2
B
, 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
=
P
h
+
2
B
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, we need to isolate it on one side of the equation.
S = Ph + 2B
Subtract 2B from both sides:
S - 2B = Ph
Divide both sides by h:
(P = (S - 2B)/h)
So the equation solved for P is:
P = (S - 2B)/h
B. We know that the height of the rectangular prism is 4 meters, the surface area is 96 square meters, and the base area is 8 square meters. We can use the equation from part A to solve for the perimeter.
P = (S - 2B)/h
P = (96 - 2(8))/4
P = (96 - 16)/4
P = 80/4
P = 20
Therefore, the perimeter of the base of the rectangular prism is 20 meters.