Question

What is the surface area of the rectangular prism? 1.8 ft 2/5 ft 1/2 ft

Answer 1

Each face of a rectangular prism has a rectangle shape. To calculate the surface area we need to calculate the area of all the faces. Each face appears twice on the prism, on opposite sides so we only need to make three calculations. These are done using the formulas below:

`\begin{gathered} A_1=height\cdot width_{} \\ A_2=length\cdot width_{} \\ A_3=length\cdot height_{} \end{gathered}`

Using the data from the problem we can calculate these areas.

`\begin{gathered} A_1=\text{ 1.8}\cdot(2)/(5)=0.72\text{ square ft} \\ A_2=(1)/(2)\cdot(2)/(5)=0.2\text{ square ft} \\ A_3=1.8\cdot(1)/(2)=0.9\text{ square ft} \end{gathered}`

The surface area of the prism is the sum of the areas above multiplied by two.

`\begin{gathered} A_{\text{surface}}=2\cdot(A_1+A_2+A_3) \\ A_{\text{surface}}=2\cdot(0.72+0.2+0.9)=2\cdot1.82=3.64\text{ square ft} \end{gathered}`