To find the surface area of the triangular prism, we first need to find the area of each of the three faces.
1. The first face is a right triangle with legs measuring 3.6 meters and 3.6 meters. The area of this face is:
Area = 0.5 * base * height
Area = 0.5 * 3.6 * 3.6
Area = 6.48 square meters
2. The second face is another right triangle with legs measuring 3.6 meters and 3.6 meters. The area of this face is the same as the first face:
Area = 6.48 square meters
3. The third face is a right triangle with a hypotenuse of 5.1 meters and legs measuring 3.6 meters and 3.6 meters. To find the height of this triangle, we can use the Pythagorean theorem:
h^2 = 5.1^2 - 3.6^2
h^2 = 26.01 - 12.96
h^2 = 13.05
h ≈ 3.6 meters
The area of this face is:
Area = 0.5 * base * height
Area = 0.5 * 3.6 * 3.6
Area = 6.48 square meters
Now, we can find the total surface area of the triangular prism by adding up the areas of the three faces:
Total Surface Area = 6.48 + 6.48 + 6.48
Total Surface Area = 19.44 square meters
Therefore, the surface area of the triangular prism formed by cutting the 2005 world record longest sandwich in half diagonally is 19.44 square meters.