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):
- The perimeter \( P \) of the triangle is \( 3.6 + 0.44 + 5.1 = 9.14 , \text{m} \).
- 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?