Question

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.

Answer 1

Given:

The surface area of a prism is given by:

$S=Ph+2B$

Where, S= surface area, P=perimeter h= height B = base area

A) Solve the equation for perimeter P of the base:

$\begin{gathered} S=Ph+2B \\ Ph=S-2B \\ P=\frac{S-2B}{h} \end{gathered}$

B) Height =4 meters

Surface area=96 square meters

Base area= 8 square meters

Calculate Perimeter

Substituting these values in equation obtained in part A

$\begin{gathered} P=\frac{96-2\times8}{4} \\ =\frac{96-16}{4} \\ =\frac{80}{4} \\ =20\text{ meters} \end{gathered}$

hence, the perimeter of the base of prism is 20 meters.