To find the surface area of the triangular prism created by cutting the sandwich in half diagonally, we need to create a net of the prism.
First, we need to visualize the triangular prism. The net of a triangular prism consists of two triangles and three rectangles. The base of the prism is a triangle, which is half of the original sandwich after cutting it diagonally. The height of the prism remains 0.44 meters while the hypotenuse of the triangle is 5.1 meters.
Next, we calculate the area of each of the shapes in the net: two triangles and three rectangles.
1. Area of the two triangles:
Since we know the base and height of the triangle, we can use the formula for the area of a triangle:
Area = 0.5 * base * height
Area = 0.5 * 3.6 * 0.44
Area = 0.792 square meters
We have two triangles, so the total area of the triangles is 2 * 0.792 = 1.584 square meters.
2. Area of the three rectangles:
The width of the sandwich is 3.6 meters and the length of the hypotenuse of the triangle (and therefore the length of the base of the prism) is 5.1 meters. So, the three rectangles have the following dimensions:
- 2 rectangles with width 3.6 meters and length 5.1 meters
- 1 rectangle with length 3.6 meters and width 0.44 meters
Calculate the area of each rectangle:
Rectangle 1: Area = 3.6 * 5.1 = 18.36 square meters
Rectangle 2: Area = 3.6 * 5.1 = 18.36 square meters
Rectangle 3: Area = 3.6 * 0.44 = 1.584 square meters
Total area of the three rectangles = 18.36 + 18.36 + 1.584 = 38.304 square meters
3. Sum of the areas of all shapes:
Total surface area = Area of two triangles + Area of three rectangles
Total surface area = 1.584 + 38.304 = 39.888 square meters
Therefore, the surface area of the triangular prism created by cutting the sandwich in half diagonally is 39.888 square meters.
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.
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