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 can first find the lateral surface area of the prism and then add the area of the two triangular bases.
The lateral surface area of a triangular prism can be calculated using the formula:
Lateral Surface Area = perimeter of base x height of prism
In this case, the perimeter of the triangular base is 5.1 meters (the hypotenuse of the triangle), and the height of the prism is 3.6 meters. So the lateral surface area is:
Lateral Surface Area = 5.1m x 3.6m = 18.36 square meters
Next, we need to find the area of the two triangular bases. The formula for the area of a triangle is:
Area = 0.5 x base x height
Since the base of the triangle is 3.6 meters and the height is 3.6 meters, we can calculate the area of one triangle:
Area of one triangle = 0.5 x 3.6m x 3.6m = 6.48 square meters
Since there are two triangular bases, the total area of the two triangles is:
Total area of two triangles = 2 x 6.48 square meters = 12.96 square meters
Finally, we can find the total surface area of the triangular prism by adding the lateral surface area and the area of the two triangular bases:
Total Surface Area = Lateral Surface Area + Total area of two triangles
Total Surface Area = 18.36 square meters + 12.96 square meters = 31.32 square meters
Therefore, the surface area of the triangular prism created by cutting the sandwich in half diagonally is 31.32 square meters.