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

1 answer

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.