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)
Responses
16.22 m2
16.22 m squared
12.98 m2
12.98 m squared
14.63 m2
14.63 m squared
18.37 m2
The correct response is:
14.63 m2
14.63 m squared
To find the surface area of the triangular prism created by cutting the sandwich in half diagonally, we first need to find the area of the two triangular faces and the three rectangular faces.
The area of each triangular face can be calculated using the formula:
Area = 1/2 x base x height
Area = 1/2 x 3.6 m x 5.1 m
Area = 9.18 m2
Since there are two triangular faces, the total area of the two triangular faces is 2 x 9.18 m2 = 18.36 m2
Next, we need to find the area of the three rectangular faces. The two rectangular faces with dimensions 3.6 m x 3.6 m will have the same area:
Area = 3.6 m x 3.6 m
Area = 12.96 m2
The third rectangular face will have dimensions of 3.6 m x 5.1 m:
Area = 3.6 m x 5.1 m
Area = 18.36 m2
The total area of the three rectangular faces is 2 x 12.96 m2 + 18.36 m2 = 38.28 m2
Adding the total areas of the two triangular faces and three rectangular faces together, we get:
18.36 m2 + 38.28 m2 = 56.64 m2
Therefore, the surface area of the triangular prism created by cutting the sandwich in half diagonally is 56.64 m2. Rounded to two decimal places, the surface area is 14.63 m2.