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 14.63 m2 14.63 m squared 16.22 m2 16.22 m squared 12.98 m2 12.98 m squared 18.37 m2
To find the surface area of the triangular prism created by cutting the sandwich in half diagonally, we first need to calculate the area of the three individual faces.
1. The two triangular faces:
The base of the triangle is the hypotenuse of the original triangle, which is 5.1 meters. The height of the triangle can be found using the Pythagorean theorem:
\(a^{2} + b^{2} = c^{2}\)
\(a^{2} + 3.6^{2} = 5.1^{2}\)
\(a^{2} + 12.96 = 26.01\)
\(a^{2} = 13.05\)
\(a \approx 3.61\)
So, the height of the triangle is approximately 3.61 meters.
The area of one of the triangular faces is:
\(0.5 \times base \times height\)
\(0.5 \times 5.1 \times 3.61\)
\(9.19 \text{ m}^{2}\)
Since there are two identical triangular faces, the total area for both triangular faces is:
\(2 \times 9.19 = 18.38 \text{ m}^{2}\)
2. The rectangular face:
The length of the rectangle is 3.6 meters, and the height can be calculated using the Pythagorean theorem:
\(3.6^{2} + h^{2} = 5.1^{2}\)
\(12.96 + h^{2} = 26.01\)
\(h^{2} = 13.05\)
\(h \approx 3.61\)
So, the height of the rectangle is also approximately 3.61 meters.
The area of the rectangular face is:
\(length \times height\)
\(3.6 \times 3.61\)
\(12.98 \text{ m}^{2}\)
Therefore, the total surface area of the triangular prism created by cutting the sandwich in half diagonally is:
\(18.38 + 12.98 = 31.36 \text{ m}^{2}\)
None of the provided answer choices match this calculation.