# Bonnie has a container in the shape of a rectangular pyramid. The formula for the surface area of...

## Question:

Bonnie has a container in the shape of a rectangular pyramid. The formula for the surface area of the enclosed space is {eq}S = lw + 0.5Ph {/eq}.

Solve for {eq}P {/eq}.

A. {eq}\; P = S - lw - 0.5h {/eq}

B. {eq}\; P = S + lw + 0.5h {/eq}

C. {eq}\;\displaystyle P = \frac{S - lw}{0.5h} {/eq}

D. {eq}\;\displaystyle P = \frac{S}{lw + 0.5h} {/eq}

## Changing Subject of an Equation:

This question is asking us to change the subject of the equation and make it P. This means that we have to rewrite the equation in such a way that P comes to one side and the rest of the equation goes to the other side.

Solving for P means making it the subject of the equation. This is done as follows.

\begin{align} &S = lw + 0.5Ph\\ &S-lw=0.5Ph&&&&\left [ \text{Subtracting }lw \text{ from both the sides} \right ]\\ &\frac{S-lw}{0.5}=Ph&&&&\left [ \text{Dividing both the sides by }0.5 \right ]\\ &\frac{S-lw}{0.5h}=P&&&&\left [ \text{Dividing both the sides by }h \right ]\\ \therefore &P=\frac{S-lw}{0.5h} \end{align}

Thus, the correct option is C.