To determine the amount of material needed to build the storage bin, we should calculate the surface area of the rectangular prism (also known as a rectangular box).
A rectangular prism has six faces:
- There are two identical faces for each pair of dimensions: length × width, width × height, and length × height.
1. Calculate the area of the two faces with dimensions length and width:
[tex]\[
\text{Area}_{\text{length × width}} = 2 \times (3.5 \, \text{ft} \times 2 \, \text{ft}) = 2 \times 7 \, \text{ft}^2 = 14 \, \text{ft}^2
\][/tex]
2. Calculate the area of the two faces with dimensions width and height:
[tex]\[
\text{Area}_{\text{width × height}} = 2 \times (2 \, \text{ft} \times 2.5 \, \text{ft}) = 2 \times 5 \, \text{ft}^2 = 10 \, \text{ft}^2
\][/tex]
3. Calculate the area of the two faces with dimensions length and height:
[tex]\[
\text{Area}_{\text{length × height}} = 2 \times (3.5 \, \text{ft} \times 2.5 \, \text{ft}) = 2 \times 8.75 \, \text{ft}^2 = 17.5 \, \text{ft}^2
\][/tex]
4. Sum all these areas to get the total material needed:
[tex]\[
\text{Total material needed} = 14 \, \text{ft}^2 + 10 \, \text{ft}^2 + 17.5 \, \text{ft}^2 = 41.5 \, \text{ft}^2
\][/tex]
Therefore, the amount of material needed to make the box is:
[tex]\[
\boxed{41.5 \, \text{ft}^2}
\][/tex]
So, the correct answer is:
A. [tex]$41.5 ft^2$[/tex]
