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)

Answer 1

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.