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.
To find the surface area of the triangular prism created by cutting the sandwich in half diagonally, we will first determine the area of each face of the prism and then add them together.
1. Calculate the area of the triangular base:
The base of the prism is a right triangle with a hypotenuse of 5.1 meters and legs that are half the width and half the thickness of the original sandwich.
Leg 1 = 0.5(3.6) = 1.8 meters
Leg 2 = 0.5(0.44) = 0.22 meters
Now, we can calculate the area of the triangular base using the formula for the area of a triangle:
Area = 0.5 * base * height
Area = 0.5 * 1.8 * 0.22
Area = 0.396 square meters
2. Calculate the area of the three rectangular sides of the prism:
There are three rectangular sides of the prism, each with dimensions that match the original dimensions of the sandwich:
Side 1: 3.6 meters x 0.44 meters = 1.584 square meters
Side 2: 3.6 meters x 0.44 meters = 1.584 square meters
Side 3: 5.1 meters x 0.44 meters = 2.244 square meters
3. Add the areas together:
Total surface area = 3 * (area of rectangular side) + (area of triangular base)
Total surface area = 3 * 1.584 + 0.396
Total surface area = 4.752 + 0.396
Total surface area = 5.148 square meters
Therefore, the surface area of the triangular prism created by cutting the sandwich in half diagonally is 5.148 square meters.