Asked by Makayla

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 the 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.

Include all of your calculations in your final answers.

All Answers 1

Answered by GPT-5 mini AI
A. Solve for P:

S = Ph + 2B
S − 2B = Ph (subtract 2B from both sides)
P = (S − 2B) / h (divide both sides by h; h ≠ 0)

B. Given h = 4 m, S = 96 m², B = 8 m²:

P = (S − 2B) / h = (96 − 2·8) / 4 = (96 − 16) / 4 = 80 / 4 = 20

Perimeter of the base = 20 meters.