Question

The 2005 world record for the longest sandwich is 3.6 meters with a width of 3.6 meters and a thickness of 0.44 meters. If you cut the sandwich in half diagonally, it would create a triangular prism with a hypotenuse of 5.1 meters. Apply the technique of using nets to find the surface area.(1 point)
Responses

16.22 m2
16.22 m squared

14.63 m2
14.63 m squared

18.37 m2
18.37 m squared

12.98 m2
12.98 m squared

Answer 1

To find the surface area of the triangular prism formed by cutting the sandwich diagonally, we first need to determine the dimensions of the triangular cross-section.

When you cut the sandwich in half diagonally, you create a right triangle where:
- One leg (width) is 3.6 meters
- Another leg (height or thickness) is 0.44 meters
- The hypotenuse, as given, is 5.1 meters.

### Step 1: Calculate the area of the triangle

The area \( A \) of the triangular cross-section is calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

For our triangle, we can take:
- Base = 3.6 meters (width)
- Height = 0.44 meters (thickness)

Substituting these values in:
\[
A = \frac{1}{2} \times 3.6 \times 0.44
\]
\[
A = \frac{1}{2} \times 1.584
\]
\[
A = 0.792 \, \text{m}^2
\]

### Step 2: Calculate the lateral area of the prism

The lateral area \( L \) of a triangular prism can be calculated by using the perimeter of the triangle multiplied by the length of the prism (length of the sandwich):
1. The perimeter \( P \) of the triangle is \( 3.6 + 0.44 + 5.1 = 9.14 \, \text{m} \).
2. Length of the prism (length of the sandwich) = 3.6 m.

Thus,
\[
L = P \times \text{length}
\]
\[
L = 9.14 \times 3.6
\]
\[
L = 32.904 \, \text{m}^2
\]

### Step 3: Calculate total surface area

The total surface area \( SA \) can be computed by adding the lateral area and the areas of the two triangular bases:
- Two triangular bases (each with an area of 0.792 m²).

So:
\[
SA = L + 2A
\]
\[
SA = 32.904 + 2 \times 0.792
\]
\[
SA = 32.904 + 1.584
\]
\[
SA = 34.488 \, \text{m}^2
\]

Hence, after checking the provided options, none match the calculated area correctly, suggesting some discrepancy in provided values. However, if I had to match it with the closest option based on a different understanding of the dimensions or other measurements, that would be necessary to re-evaluate.

Can you please confirm the correctness of provided sizes or data in the problem statement?