Question

Carlos needs to paint the outside of the shed in his backyard, including its roof but not including its floor.

A rectangular prism with a length of 8 feet, width of 5 feet, and height of 6 feet.

What is the total area of the surfaces that he needs to paint?
214 feet squared
230 feet squared
300 feet squared
350 feet squared

Answer 1

To determine the total area of the surfaces that Carlos needs to paint on the shed, which is in the shape of a rectangular prism (cuboid), we need to calculate the surface area excluding the floor.

### Given dimensions:
- Length (L) = 8 feet
- Width (W) = 5 feet
- Height (H) = 6 feet

### Surface area of a rectangular prism:
The total surface area \( A \) of a rectangular prism is given by:
\[
A = 2(LW + LH + WH)
\]

However, since we only want to paint the walls and the roof, we don't need to include the floor area in our calculations.

### Walls:
The area of the walls (4 sides):
- Two sides of dimensions \( H \times L \) (2 walls)
- Two sides of dimensions \( H \times W \) (2 walls)

Calculating the area of the walls:
- Area of the two walls (H × L):
\[
2 \times (H \times L) = 2 \times (6 \times 8) = 2 \times 48 = 96 \, \text{sq ft}
\]
- Area of the two walls (H × W):
\[
2 \times (H \times W) = 2 \times (6 \times 5) = 2 \times 30 = 60 \, \text{sq ft}
\]

Total area of the walls:
\[
A_{\text{walls}} = 96 + 60 = 156 \, \text{sq ft}
\]

### Roof:
The area of the roof (top rectangle):
\[
\text{Area of the roof} = L \times W = 8 \times 5 = 40 \, \text{sq ft}
\]

### Total area to be painted:
Now, we add the area of the walls and the area of the roof:
\[
A_{\text{total}} = A_{\text{walls}} + A_{\text{roof}} = 156 + 40 = 196 \, \text{sq ft}
\]

### Conclusion:
It appears I've made a mistake here. Let's double-check the entire problem.
To find the total surface area again:

Painted surfaces only include the walls and the roof:
1. Walls (2 × 8 × 6) + (2 × 5 × 6) = 96 + 60 = 156
2. Roof (8 × 5) = 40
So total = 196 sq ft.

However, that option is not among the available answers. Conflict in options suggests reconsideration of dimensions or inclusion.

After recalculating your premise, none fits the exclusive painting.

For verification, it appears discrepancy exists thus confirming:
- 214 (Area to Include?)
- 230 (Wall/roof other metrics?)
- 300 (Reject excess)
- 350 (Excessive)

Ultimately, assuming canvassing is per-listed specification, revise dimensional input base.

Nonetheless, original computed:
\[
\text{Total Area} = 196 \text{ ft squared.}
\]
Since other listed fits require specification, assert checking reinstated.