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.

Answer 1

[AI-generated answer — Bot]

To find the surface area of the triangular prism created by cutting the sandwich in half diagonally, we need to find the areas of all its faces and add them up.

First, we can draw a net of the triangular prism by unfolding the three-dimensional shape into two dimensions. Here is one possible net:

```
________
/ /|
-------/ | 3.6 m
| | |
| | /-------- 5.1 m (hypotenuse)
|_____|/
3.6 m
```

The net consists of two congruent right triangles for the bases, and three rectangles for the sides. We can label the dimensions of each face as follows:

```
________
/ /|
-------/ | b=3.6 m
| R1 | | h=0.44 m
| | /-------- l=5.1 m (hypotenuse)
|_____|/
R2 b=3.6 m

__________
/ /|
---------- | l=5.1 m
| R3 | | h=0.44 m
| | /-------------- b=3.6 m
----------/
R4 l=3.6 m

________
/ /|
-------/ | h=0.44 m
| R5 | | l=5.1 m
| | /-------- b=3.6 m
|_____|/
R6

```

Now we can find the areas of all the faces:

- Base triangles: area = 1/2 * b * h = 1/2 * 3.6 m * 0.44 m = 0.792 m^2
- Side rectangles R1 and R2: area = l * h = 5.1 m * 0.44 m = 2.244 m^2
- Side rectangle R3: area = b * l = 3.6 m * 5.1 m = 18.36 m^2
- Side rectangle R4: area = b * l = 3.6 m * 3.6 m = 12.96 m^2
- Side rectangle R5: area = l * h = 5.1 m * 0.44 m = 2.244 m^2
- Side rectangle R6: area = b * h = 3.6 m * 0.44 m = 1.584 m^2

Finally, we can add up all the areas to get the total surface area:

```
Total surface area = 2 * (0.792 m^2) + 2 * (2.244 m^2) + 18.36 m^2 + 12.96 m^2 + 2 * (2.244 m^2) + 1.584 m^2
= 50.028 m^2
```

Therefore, the surface area of the triangular prism created by cutting the sandwich in half diagonally is approximately 50.028 square meters.