To find the surface area of the triangular prism formed by cutting the sandwich in half diagonally, we need to calculate the area of each of the three faces (two triangles and one rectangle) and then add them together.
1. Area of the rectangle face:
The length of the rectangle face is equal to the width of the original sandwich (3.6 meters) and the width is equal to the thickness of the sandwich (0.44 meters). So the area of the rectangle face is:
Area = length x width = 3.6 meters x 0.44 meters = 1.584 square meters
2. Area of the first triangular face:
The base of the triangle is the hypotenuse of the triangle formed by cutting the sandwich in half diagonally (5.1 meters) and the height can be calculated using the Pythagorean theorem.
Height = √(5.1^2 - 3.6^2) = √(26.01 - 12.96) = √13.05 ≈ 3.61 meters
So the area of the first triangular face is:
Area = 0.5 x base x height = 0.5 x 5.1 meters x 3.61 meters ≈ 9.191 square meters
3. Area of the second triangular face:
Since the two triangular faces are congruent, the area of the second triangular face is also approximately 9.191 square meters.
Therefore, the total surface area of the triangular prism formed by cutting the sandwich in half diagonally is:
Total Surface Area = 2 x Area of a triangle + Area of rectangle
Total Surface Area ≈ 2 x 9.191 square meters + 1.584 square meters
Total Surface Area ≈ 18.382 + 1.584
Total Surface Area ≈ 19.966 square meters
So, the surface area of the triangular prism formed by cutting the sandwich in half diagonally is approximately 19.966 square meters.
answer my 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 meter, find the surface area.
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